Pith. sign in

REVIEW 3 major objections 4 minor 221 references

Thermal Correlators and Black Holes: From Infinity to Singularity

T0 review · 3 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The stress-tensor sector of a thermal correlator carries poles that mark the black hole singularity.

desk verdict A technically rich thesis whose headline singularity claim rests on a numerical fit that still needs error control. read the letter →

arxiv 2508.17139 v1 pith:ZSMF3ZWT submitted 2025-08-23 hep-th cond-mat.stat-mechgr-qc

Samuel Valach This is my paper · ORCID
classification hep-thcond-mat.stat-mechgr-qc PACS 11.25.Tq04.70.Dy
keywords AdS/CFTcorrespondencethermalcorrelatorsblackholesingularitynear-boundaryexpansionstress-tensorsectorbouncingsingularitiesaveragednullenergyconditionGauss-Bonnetgravity
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This thesis argues that the deep interior geometry of a black hole, down to its singularity, is encoded in a purely boundary quantity: the stress-tensor sector of a thermal two-point function. Resumming the OPE contributions from the stress tensor and its composites produces branch-point-like poles in complex time, located precisely where bulk geodesics that pass the horizon, bounce off the singularity, and return to the boundary would end. At finite conformal dimension the poles sit at $\tau_c = (\beta/\sqrt{2})e^{i\pi/4} + ik\pi/2$ in $d=4$ with exponent $2\Delta-2$; in the large-dimension limit the same sector reproduces the geodesic proper length and its branch point at $\tau=\beta/2$. A second line of results shows that thermal stress-tensor correlators in pure-gravity duals become universal near the lightcone, with the bulk Lagrangian entering only through three parameters, and that saturating the averaged null energy condition makes the correlator independent of temperature. The combined picture makes thermal correlators, especially the stress-tensor sector, sensitive probes of black hole interiors and causality constraints.

What carries the argument

The load-bearing object is the stress-tensor sector of the boundary OPE: the set of multi-stress-tensor primary operators $[T^n]_J$ (spin $J=0,2,\ldots,2n$, dimension $dn$ at leading order) and their descendants. On the bulk side the machinery is the near-boundary expansion of the bulk-to-boundary propagator, $\Phi_T = (r/w^2)^\Delta\left(1 + \sum a_{m,k}^{(n)}\rho^{2m}w^{2k} r^{-dn}\right)$, which determines the OPE coefficients $\Lambda_n$ order by order in $1/r$. The argument is carried by the asymptotic large-$n$ form $\Lambda_n \approx c(\Delta)\, n^{2\Delta-3}(1/\sqrt{2})^{4n}e^{i\pi n}$, whose resummation by an integral produces a logarithm whose vanishing locus is the pole set; the same OPE data, when the large-$\Delta$ limit is taken first, yields the branch point of the geodesic length. For the second theme, the machinery is the reduction of linearized Einstein and Gauss-Bonnet perturbations to three channels (scalar, shear, sound), integrated over two spatial directions so the equations collapse to three gauge-invariant PDEs whose near-lightcone solutions are described by three universal functions.

What would settle it

Compute the stress-tensor sector $G_T(\tau)$ at larger $n$ without relying on the fitted asymptotic form, for example with high-precision recursion or an independent bootstrap calculation, and check whether the pole at $\tau_c = (\beta/\sqrt{2})e^{i\pi/4}$ survives with the predicted exponent $2\Delta-2$; alternatively, consider a nonsingular spacetime such as a star that shares the same near-boundary expansion and test whether the same pole appears, since its presence would mean the pole is not a singularity diagnostic.

Watch

Extended reading notes

Core claim

In a holographic CFT dual to Einstein gravity, the thermal two-point function of a scalar splits into a stress-tensor sector, built from multi-stress-tensor operators $[T^n]_J$, and a double-trace sector. The central claim is that the stress-tensor sector alone knows about the curvature singularity: after resumming the large-$n$ OPE coefficients, the $d=4$ correlator $G_T(\tau)$ develops singularities at $\tau_c = (\beta/\sqrt{2})e^{i\pi/4} + ik\pi/2$ with $G_T(\tau)\propto (\tau-\tau_c)^{-(2\Delta-2)}$, precisely the locations and exponents predicted by geodesics that cross the horizon, reflect off the singularity, and return to the boundary. The double-trace sector is then forced to carry the same singularity with the opposite sign, so that the full correlator satisfies KMS and remains analytic in the physical strip; this explains why the bouncing singularity is invisible in the full correlator while still being present in the sector. In the large-$\Delta$ limit the finite-$\Delta$ pole is replaced by a branch point of $-(1/\Delta)\log G_T(\tau)$ at $\tau=\beta/2$, matching the bulk geodesic length, with the order of the $\tau\to\tau_c$ and $\Delta\to\infty$ limits controlling which description applies. For pure-gravity duals, the thesis further establishes near-lightcone universality of stress-tensor two-point functions in Einstein and Gauss-Bonnet gravity, where three universal functions describe the correlator and the bulk action enters only through corrections to cubic stress-tensor couplings and the thermal one-point function; when an averaged null energy condition is saturated, the near-lightcone correlator takes the vacuum form and becomes temperature-independent.

Load-bearing premise

The load-bearing premise is that the near-boundary expansion gives the full stress-tensor sector of the bulk solution from the AdS boundary down to $r=0$, so the boundary OPE data uniquely fixes the analytic structure that corresponds to the interior geometry, and that the numerically fitted large-$n$ OPE coefficients control the resummation that produces the poles.

Editorial extensions

If this is right

  • A boundary CFT calculation of multi-stress-tensor OPE data can locate the black hole singularity in complex time without reconstructing the bulk geometry.
  • Double-trace operators are not optional: they are required to restore KMS and analyticity, and their singularity must cancel the stress-tensor pole, so the full correlator's analytic structure determines them from the universal sector.
  • The map between OPE sectors and bulk geodesics explains the noncommutativity of the large-dimension and near-singularity limits: the finite-$\Delta$ pole disappears into the branch point at $\tau=\beta/2$ as $\Delta\to\infty$.
  • In pure-gravity duals, the near-lightcone stress-tensor correlator is universal across Einstein and Gauss-Bonnet gravity up to three parameters, so higher-derivative corrections affect it only through those parameters.
  • Saturating an averaged null energy condition forces the near-lightcone correlator to the vacuum form and makes it temperature-independent, which implies saturation of all higher-spin averaged null energy conditions for that polarization.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A nonsingular star with the same asymptotic metric shares the same near-boundary data, so the stress-tensor sector should be identical; all information about the interior would then live in the double-trace sector, a prediction that could be tested against an explicit star solution.
  • The same pole-tracking logic gives an observable signature of singularity resolution: finite-coupling corrections should move or smear the pole at $\tau_c$, so locating it at higher orders would expose how stringy or loop corrections modify the interior.
  • The extra singularities noted in the paper for $d=6$ and $d=8$ (at $\tau=\beta$ and at $\frac{\beta}{2}e^{\pm i\pi/8}/\sin(\pi/8)$ respectively) may correspond to geodesic families not present in $d=4$, or to non-geodesic saddles; identifying their bulk origin would be a natural extension.
  • The numerical fit that fixes $c(\Delta)$ could be replaced by a bootstrap consistency check: truncating the spectrum to multi-stress tensors and double traces and imposing crossing plus KMS should force the predicted pole location and exponent if the claim is correct.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. This PhD thesis studies thermal two-point functions in holographic CFTs, using the near-boundary expansion as the main tool. Chapter 3 makes the central claim that the stress-tensor sector of a thermal scalar correlator encodes information about the black hole singularity: in d=4, after resumming multi-stress-tensor OPE contributions, the sector develops poles at tau_c = (beta/sqrt{2}) e^{i pi/4} + i k pi/2 with scaling 1/(tau-tau_c)^{2 Delta - 2}, matching bouncing geodesics that reflect off the singularity. Chapters 4-6 compute thermal stress-tensor two-point functions in Einstein and Gauss-Bonnet gravity, extract anomalous dimensions and OPE data for double-stress tensors, identify three universal functions controlling the near-lightcone behavior, and show that saturation of an ANEC makes the corresponding near-lightcone correlator temperature-independent.

Significance. If the Chapter 3 claim is correct, it is a significant step: it provides a concrete boundary observable that encodes the black hole interior singularity, and it links the resummation of the stress-tensor sector to geodesic probes on the second sheet. The result is universal in the sense that it does not depend on the details of the probe operator. The Chapters 4-6 results are also valuable: they provide explicit CFT data for double-stress tensors in holographic theories, verify consistency with conformal collider bounds, and exhibit a clean universality structure near the lightcone, including the temperature-independence that follows from ANEC saturation. The thesis contains many non-trivial checks against geodesic calculations, CFT conformal blocks, and independent OPE results, and the appendices provide substantial technical detail. The central Chapter 3 derivation, however, rests on numerically fitted large-n OPE coefficients without error bars and on an explicitly flagged assumption about the validity of the near-boundary expansion in the interior, so the headline claim is not yet established to the standard expected for a journal publication.

major comments (3)
  1. [Sec. 3.3.3, Eqs. (3.55)-(3.60)] The central singularity claim is obtained from the fitted large-n form Lambda_n^a = c(Delta) n^{2 Delta - 3} (1/sqrt{2})^{4n} e^{i pi n}, with c(Delta) determined only up to a reported ~2% accuracy and with no error bars quoted for the exponents in (3.72). The integral approximation (3.58) then produces the pole (3.60) with exponent 2 Delta - 2. This chain is load-bearing: a subleading 1/n correction or a slightly different power n^{alpha} would change the exponent and could shift the location tau_c, invalidating the quantitative match to the bouncing geodesic result (3.41)-(3.42). The manuscript does not provide an error estimate for the resummation, and the fit window n <= 50 with a crossover at n* = Delta/2 means that the finite-Delta regime where the claim is made is precisely where the fit is most delicate, especially near integer Delta where c(Delta) has poles (3.56). Without an independent check of the large-n asymptotics, or a quantified bound on the 1/n corrections, Eq. (3.60) should be regarded as a numerically motivated conjecture rather than an established result.
  2. [Sec. 3.5.3, item 6] The author explicitly flags the hidden working assumption that the near-boundary expansion (2.76) reliably solves the Klein-Gordon equation in the region r in (0, infinity). This assumption is load-bearing for the thesis's main claim, because the OPE coefficients Lambda_n are extracted from that expansion; if the near-boundary expansion fails in the interior, the fitted Lambda_n are not the physical OPE data, and the geodesic match in Sec. 3.3.5 is unsupported. The manuscript should supply evidence for this assumption, for example by comparing the near-boundary solution with a full numerical solution of the bulk equation of motion, or by estimating the radius of convergence of the 1/r expansion. The current discussion in Sec. 3.5.3 item 6 only notes the issue for the star example and does not test the Schwarzschild-AdS case where the assumption is actually used.
  3. [Sec. 3.3.5 and Sec. 3.4.2] The transition from the finite-Delta bouncing singularity to the large-Delta branch point at tau = beta/2 is argued through a noncommutativity of limits, but the argument is not a derivation. In particular, the identification in (3.87), which determines L_[phi phi] and bL from the branch-point function fT(y), is assumed from the geodesic side rather than derived from the OPE data. The large-Delta fit uses Delta = (10^8 + 1)/2 and estimates L_n with 1/Delta corrections, but the quoted uncertainties in (3.72) are small yet unquantified in their effect on the branch-point location and prefactor in (3.75). Given that the agreement with the geodesic result (3.76) is excellent, this is not an objection to the result itself, but the manuscript should state more clearly which parts of Sec. 3.4 are conjectural and which follow from the OPE data alone.
minor comments (4)
  1. [Sec. 3.3.3, Fig. 3.6] Figure 3.6 plots ratios of explicit Lambda_n to the leading large-n form, but the figure does not show error bars or the n-range used for the fit; adding both would help the reader judge the stability of (3.55).
  2. [Sec. 3.3.4, Eq. (3.72)] The fit results log a = 4 log 2 +/- 10^{-6}, b = -7/3 +/- 10^{-4}, log c = -2.050 +/- 10^{-3} are quoted without a statement of the fitting procedure or the covariance of the errors; please specify the fit range and the treatment of 1/n and 1/Delta corrections.
  3. [Sec. 2.3, Eq. (2.83)] The relation b_{T_mu nu}/beta^4 = - mu C_T S_4 / 40 introduces mu on the right and mu is also used for the bulk mass parameter; the two uses are related but the notation is confusing. A brief comment distinguishing them would improve readability.
  4. [Sec. 4.3.5, Eqs. (4.94)-(4.95)] The extraction of the anomalous dimensions gamma_J^{(1)} relies on comparing three polarizations with a common solution; please state explicitly whether the solution (4.94)-(4.95) is unique, or whether the remaining freedom in the rho^{(1)} coefficients could change gamma_J^{(1)}.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the singularity prediction is derived from computed OPE coefficients and cross-checked against independent geodesic calculations; the main caveats are numerical fit control and an explicitly flagged near-boundary assumption.

full rationale

The central claim of Chapter 3 is not circular. The bouncing singularity at (3.59)-(3.60) is obtained by solving the bulk Klein-Gordon equation with the near-boundary ansatz, computing OPE coefficients Lambda_n (Eqs. 3.50-3.51), fitting their large-n form (3.55), and resumming the OPE as an integral (3.58). The geodesic singularity in Sec. 3.2 is derived independently from the geodesic equation in the same bulk metric, so the match is a genuine cross-check rather than a reduction of one computation to the other. No parameter is fitted to the target singularity itself, so the 'fitted input called prediction' pattern does not apply. The author explicitly flags the main limitation: 'a hidden working assumption used in this chapter is that the near-boundary expansion provides a reliable solution to the Klein-Gordon equation in the region r in (0,infty)' (Sec. 3.5.3, item 6), and the large-n fit is presented without quoted error bars. These are correctness and robustness caveats, not circular reasoning. Self-citations to [1-4] are declarations of co-authorship; the derivations are reproduced in the thesis and are checked against external results ([13,14,30,56-60]), so the self-citations are not load-bearing. Chapters 4-6 compare bulk and conformal-block computations to extract CFT data; the matching procedure is a holographic dictionary check, not a definitional equivalence. Overall the derivation chain is self-contained and not circular.

Assumptions & free parameters 3 free parameters · 7 assumptions · 0 invented entities

The central claims rest on standard AdS/CFT assumptions plus the near-boundary ansatz, which the author himself flags as a hidden working assumption. The novel results depend on numerically fitted OPE coefficients and on subleading CFT data that is only partially determined. No new particles, forces, or dimensions are introduced.

free parameters (3)
  • Asymptotic large-n form of OPE coefficients Λ_n^a = Λ_n^a = c(Δ) n^{2Δ-3} (1/√2)^{4n} e^{iπn}
    Used to resum the stress-tensor sector and locate the finite-Δ bouncing singularity; the exponent 2Δ-3, base 1/√2 and phase e^{iπn} are extracted from numerical data for n up to ~50 (Sec. 3.3.3).
  • Amplitude function c(Δ) = c(Δ) = π Δ (Δ-1)/sin(πΔ) × bc(Δ), with bc(Δ) ≈ Δ/Γ(2Δ+3/2) × 4^{2Δ}/20 (valid to ~2% for Δ ≳ 5/4 and Δ ≲ 15)
    Determines the strength of the bouncing singularity in Eq. (3.60); fitted to numerically computed Λ_n for finite Δ.
  • Large-Δ L_n fit constants (a, b, c) = log a = 4 log 2, b = -7/3, log c = -2.050 (with stated uncertainties 10^-6, 10^-4, 10^-3)
    Control the branch point exponent and prefactor of L_T at τ = β/2 in the Δ→∞ limit; obtained from data at Δ = (10^8+1)/2, Eqs. (3.70)-(3.72).
assumptions (7)
  • domain assumption AdS/CFT correspondence: thermal states of the boundary CFT are dual to AdS-Schwarzschild (or Gauss-Bonnet) black holes in the bulk, with the boundary generating functional equal to the bulk on-shell action.
    Used throughout; Chapters 2-6 rely on the standard holographic dictionary (Eqs. 2.47-2.52) without derivation.
  • ad hoc to paper The near-boundary ansatz (2.76) is complete and reliable for the stress-tensor sector, including as r→∞ and presumably into the interior.
    This is the computational engine of the thesis; the author explicitly flags in Sec. 3.5.3 (future perspective 6) that 'a hidden working assumption used in this chapter is that the near-boundary expansion provides a reliable solution to the Klein-Gordon equation in the region r∈(0,∞)'.
  • domain assumption The OPE of the thermal two-point function converges uniformly in Δ for |τ|<β/2, allowing exchange of the OPE sum and the Δ→∞ limit; beyond that, the order of limits matters.
    Central to the boundary interpretation in Sec. 3.4; the Moore-Osgood argument in the GFF example (Sec. 3.4.4) supports non-exchangeability, but the general holographic case is assumed.
  • domain assumption In holographic CFTs (large central charge CT and large gap), only the stress-tensor sector and double-trace sector contribute to the scalar two-point function at the order computed, and the two sectors decouple for non-integer Δ.
    Used to split G(τ) = GT(τ) + G[ϕϕ](τ) and to justify the OPE data extraction in Chapters 2-3.
  • domain assumption Multi-stress-tensor operators thermalize in heavy states to leading order in 1/CT (Eq. 2.81), so that thermal one-point functions can be expressed in terms of heavy-state data with the black hole mass parameter μ.
    This relation is imported from [46] and used throughout Chapters 4-6 to translate bulk μ into boundary CFT data.
  • ad hoc to paper Gauss-Bonnet gravity, despite being non-unitary as a full theory, correctly captures the near-lightcone and ANEC-saturation physics of holographic CFTs; unitarity violations occur only at small impact parameter.
    Stated in Sec. 5.1 to justify using GB gravity to study ANEC saturation; this is a working assumption, not proven in the thesis.
  • domain assumption For d=2, the BTZ orbifold singularity is invisible to the thermal two-point functions considered, and G(τ)=GT(τ) with no double-trace contributions for the plane.
    Used in Chapter 3 to contrast d=2 with d≥3; relies on the Virasoro vacuum block structure (Appendix D).

how reviews work

0 comments
Cite this review

Pith. "Pith review of Thermal Correlators and Black Holes: From Infinity to Singularity." pith.science (2026). https://pith.science/paper/ZSMF3ZWT

@misc{pith2026250817139,
  author       = {Pith},
  title        = {Pith review of: Thermal Correlators and Black Holes: From Infinity to Singularity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZSMF3ZWT}},
  note         = {Machine review of arXiv:2508.17139}
}
read the original abstract

This thesis explores thermal correlation functions in conformal field theories (CFTs) and their connection to black hole geometry within the AdS/CFT correspondence, using a near-boundary expansion as the main tool. Two themes are examined. First, we show that the stress-tensor sector of boundary correlators encodes information about black hole singularities. By resumming contributions from the stress-tensor and its composites, we uncover branch-point singularities in complex time, corresponding to bulk geodesics that cross the horizon, reflect off the singularity, and return to the boundary. We further clarify the role of double-trace operators in restoring analyticity and the KMS condition, and establish a map between bulk geodesics and OPE sectors of the thermal correlator. Second, we study thermal stress-tensor correlators in CFTs with pure gravity duals. Through holographic calculations in Einstein and Gauss-Bonnet gravity, we identify a robust universal behaviour - near the lightcone the correlators are described by three universal functions. The bulk Lagrangian only affects the arguments of these functions through corrections to the cubic stress-tensor couplings and the thermal stress-tensor one-point function. We relate this behaviour to causality constraints such as the averaged null energy condition (ANEC), showing that ANEC saturation makes the correlator temperature-independent. Overall, our results demonstrate that thermal correlators - especially their stress-tensor sector - serve as sensitive probes of black hole interiors, causality, and universality in holographic CFTs.

Figures

Figures reproduced from arXiv: 2508.17139 by the authors.

Figure 3.1
Figure 3.1. The Penrose diagram for the Lorentzian section of the maximally ex [PITH_FULL_IMAGE:figures/full_fig_p035_3_1.png] view at source ↗
Figure 3.2
Figure 3.2. Diagrams for the Euclidean section (left) and the Lorentzian section [PITH_FULL_IMAGE:figures/full_fig_p036_3_2.png] view at source ↗
Figure 3.3
Figure 3.3. Plots for Λ4 and Λ5 as functions of ∆. These OPE coefficients have poles at ∆ = 2, 3, . . . , 2n and are regular for ∆ > 2n. Namely, as n grows, these coefficients become more complicated functions of ∆. For example, the first few terms in the small τ expansion of the correlator are given by GT (τ ) ≈ 1 τ 2∆ " 1 + π 4 ∆ 40  τ β 4 + π 8 ∆ [PITH_FULL_IMAGE:figures/full_fig_p042_3_3.png] view at source ↗
Figures from the paper (10 more)
Figure 3.4
Figure 3.4. Figure 3.4: On the left we plot the values of log |Λn| for ∆ = 75 2 . We see that at n∗ = 19, there is a change of behaviour of the OPE coefficients. On the right, we plot the behaviour of n∗ as a function of ∆ and find that n∗ = ∆/2 (red) [PITH_FULL_IMAGE:figures/full_fig_p043…
Figure 3.5
Figure 3.5. Figure 3.5: The value of stress-tensor contribution to the thermal correlator for [PITH_FULL_IMAGE:figures/full_fig_p043_3_5.png]
Figure 3.6
Figure 3.6. Figure 3.6: Ratio of the explicit results for Λn to the leading large-n prediction for different values of ∆ in d = 4. 3.3.3 Asymptotic analysis of OPE coefficients for finite ∆ and bouncing singularities Let us now focus on the analysis of the coefficients Λn for large values o…
Figure 3.7
Figure 3.7. Figure 3.7: Numerical data for bc(∆) (blue) compared with the function given in (3.56) (red). residual function can be approximated by19 bc(∆) ≈ ∆ Γ [PITH_FULL_IMAGE:figures/full_fig_p045_3_7.png]
Figure 3.8
Figure 3.8. Figure 3.8: The poles of the stress-tensor sector of the thermal correlator in four [PITH_FULL_IMAGE:figures/full_fig_p046_3_8.png]
Figure 3.9
Figure 3.9. Figure 3.9: The values of log [PITH_FULL_IMAGE:figures/full_fig_p047_3_9.png]
Figure 3.10
Figure 3.10. Figure 3.10: Comparing the holographic data for ∆ = (108 + 1)/2 to the ansatz (3.70) and the numerical data given by (3.72). The first few Ln are given implicitly in (3.65). For higher values of n, we again analyse the data for large but fixed ∆. For some ∆, we plot the values o…
Figure 3.11
Figure 3.11. Figure 3.11: τ as function of Ee obtained from the Euclidean geodesic analysis for the boundary theory on a sphere [PITH_FULL_IMAGE:figures/full_fig_p057_3_11.png]
Figure 6.1
Figure 6.1. Figure 6.1: The real part of f(α). The upper (solid, red) line corresponds to the scalar channel. The middle (dotted, green) line corresponds to the sound channel. The bottom (dashed, blue) line corresponds to the shear channel. At large α, all three lines approach the expected …
Figure 6.2
Figure 6.2. Figure 6.2: The imaginary part of f(α). The upper (dashed, blue) line corresponds to the shear channel. The middle (dotted, green) line corresponds to the sound channel. The bottom (solid, red) line corresponds to the scalar channel. 6.5.2 Imaginary part of correlators from WKB …

Review history (2 revisions) →

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

221 extracted references · 8 canonical work pages

  1. [1]

    Karlsson, A

    R. Karlsson, A. Parnachev, V. Prilepina, and S. Valach,Thermal stress tensor correlators, OPE and holography, JHEP 09 (2022) 234, [arXiv:2206.05544]

    arXiv 2022

  2. [2]

    Huang, R

    K.-W. Huang, R. Karlsson, A. Parnachev, and S. Valach,Freedom near lightcone and ANEC saturation, JHEP 05 (2023) 065, [arXiv:2210.16274]

    arXiv 2023

  3. [3]

    Esper, K.-W

    C. Esper, K.-W. Huang, R. Karlsson, A. Parnachev, and S. Valach,Thermal stress tensor correlators near lightcone and holography, JHEP 11 (2023) 107, [arXiv:2306.00787]

    arXiv 2023

  4. [4]

    Čeplak, H

    N. Čeplak, H. Liu, A. Parnachev, and S. Valach,Black Hole Singularity from OPE, JHEP 10 (2024) 105, [arXiv:2404.17286]

    arXiv 2024

  5. [5]

    J. D. Bekenstein,Black holes and entropy, Phys. Rev. D7 (1973) 2333–2346

    1973

  6. [6]

    S. W. Hawking,Black Holes and Thermodynamics, Phys. Rev. D13 (1976) 191–197

    1976

  7. [7]

    S. W. Hawking,Particle Creation by Black Holes, Commun. Math. Phys.43 (1975) 199–220. [Erratum: Commun.Math.Phys. 46, 206 (1976)]

    1975

  8. [8]

    J. M. Maldacena,The Large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys.2 (1998) 231–252, [hep-th/9711200]

    arXiv 1998

Show all 221 references
  1. [9]

    S. S. Gubser, I. R. Klebanov, and A. M. Polyakov,Gauge theory correlators from noncritical string theory, Phys. Lett. B428 (1998) 105–114, [hep-th/9802109]

    1998 arXiv

  2. [10]

    Witten,Anti-de Sitter space and holography, Adv

    E. Witten,Anti-de Sitter space and holography, Adv. Theor. Math. Phys.2 (1998) 253–291, [hep-th/9802150]

    1998 arXiv

  3. [11]

    Louko, D

    J. Louko, D. Marolf, and S. F. Ross,On geodesic propagators and black hole holography, Phys. Rev. D62 (2000) 044041, [hep-th/0002111]

    2000 arXiv

  4. [12]

    Kraus, H

    P. Kraus, H. Ooguri, and S. Shenker,Inside the horizon with AdS / CFT, Phys. Rev. D67 (2003) 124022, [hep-th/0212277]

    2003 arXiv

  5. [13]

    Fidkowski, V

    L. Fidkowski, V. Hubeny, M. Kleban, and S. Shenker,The Black hole singularity in AdS / CFT, JHEP 02 (2004) 014, [hep-th/0306170]

    2004 arXiv

  6. [14]

    Festuccia and H

    G. Festuccia and H. Liu,Excursions beyond the horizon: Black hole singularities in Yang-Mills theories. I., JHEP 04 (2006) 044, [hep-th/0506202]. 120

    2006 arXiv

  7. [15]

    Festuccia and H

    G. Festuccia and H. Liu,The Arrow of time, black holes, and quantum mixing of large N Yang-Mills theories, JHEP 12 (2007) 027, [hep-th/0611098]

    2007 arXiv

  8. [16]

    Amado and C

    I. Amado and C. Hoyos-Badajoz,AdS black holes as reflecting cavities, JHEP 09 (2008) 118, [arXiv:0807.2337]

    2008 arXiv

  9. [17]

    Hartman and J

    T. Hartman and J. Maldacena,Time Evolution of Entanglement Entropy from Black Hole Interiors, JHEP 05 (2013) 014, [arXiv:1303.1080]

    2013 arXiv

  10. [18]

    Liu and S

    H. Liu and S. J. Suh,Entanglement Tsunami: Universal Scaling in Holographic Thermalization, Phys.Rev.Lett.112 (2014) 011601, [arXiv:1305.7244]

    2014 arXiv

  11. [19]

    Liu and S

    H. Liu and S. J. Suh,Entanglement growth during thermalization in holographic systems, Phys.Rev. D89 (2014), no. 6 066012, [arXiv:1311.1200]

    2014 arXiv

  12. [20]

    Grinberg and J

    M. Grinberg and J. Maldacena,Proper time to the black hole singularity from thermal one-point functions, JHEP 03 (2021) 131, [arXiv:2011.01004]

    2021 arXiv

  13. [21]

    Rodriguez-Gomez and J

    D. Rodriguez-Gomez and J. G. Russo,Correlation functions in finite temperature CFT and black hole singularities, JHEP 06 (2021) 048, [arXiv:2102.11891]

    2021 arXiv

  14. [22]

    Leutheusser and H

    S. Leutheusser and H. Liu,Emergent Times in Holographic Duality, Phys. Rev. D108 (2023), no. 8 086020, [arXiv:2112.12156]

    2023 arXiv

  15. [23]

    de Boer, D

    J. de Boer, D. L. Jafferis, and L. Lamprou,On black hole interior reconstruction, singularities and the emergence of time, arXiv:2211.16512

    arXiv

  16. [24]

    J. R. David and S. Kumar,Thermal one point functions, large d and interior geometry of black holes, JHEP 03 (2023) 256, [arXiv:2212.07758]

    2023 arXiv

  17. [25]

    G. T. Horowitz, H. Leung, L. Queimada, and Y. Zhao,Boundary signature of singularity in the presence of a shock wave, arXiv:2310.03076

    arXiv

  18. [26]

    Parisini, K

    E. Parisini, K. Skenderis, and B. Withers,The Ambient Space Formalism, arXiv:2312.03820

    arXiv

  19. [27]

    Dodelson, C

    M. Dodelson, C. Iossa, R. Karlsson, A. Lupsasca, and A. Zhiboedov,Black hole bulk-cone singularities, arXiv:2310.15236

    arXiv

  20. [28]

    S. W. Hawking and D. N. Page,Thermodynamics of Black Holes in anti-De Sitter Space, Commun. Math. Phys.87 (1983) 577

    1983

  21. [29]

    Witten,Anti-de Sitter space, thermal phase transition, and confinement in gauge theories, Adv

    E. Witten,Anti-de Sitter space, thermal phase transition, and confinement in gauge theories, Adv. Theor. Math. Phys.2 (1998) 505–532, [hep-th/9803131]

    1998 arXiv

  22. [30]

    A. L. Fitzpatrick and K.-W. Huang,Universal Lowest-Twist in CFTs from Holography, JHEP 08 (2019) 138, [arXiv:1903.05306]

    2019 arXiv

  23. [31]

    Kovtun, D

    P. Kovtun, D. T. Son, and A. O. Starinets,Holography and hydrodynamics: Diffusion on stretched horizons, JHEP 10 (2003) 064, [hep-th/0309213]. 121

    2003 arXiv

  24. [32]

    Kovtun, D

    P. Kovtun, D. T. Son, and A. O. Starinets,Viscosity in strongly interacting quantum field theories from black hole physics, Phys. Rev. Lett.94 (2005) 111601, [hep-th/0405231]

    2005 arXiv

  25. [33]

    D. A. Teaney,Viscous Hydrodynamics and the Quark Gluon Plasma, p. 207–266. WORLD SCIENTIFIC, Feb., 2010.arXiv:0905.2433

    2010 arXiv

  26. [34]

    Heinz and R

    U. Heinz and R. Snellings,Collective flow and viscosity in relativistic heavy-ion collisions, Ann. Rev. Nucl. Part. Sci.63 (2013) 123–151, [arXiv:1301.2826]

    2013 arXiv

  27. [35]

    Buchel and J

    A. Buchel and J. T. Liu,Universality of the shear viscosity in supergravity, Phys. Rev. Lett.93 (2004) 090602, [hep-th/0311175]

    2004 arXiv

  28. [36]

    Iqbal and H

    N. Iqbal and H. Liu,Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm, Phys. Rev. D79 (2009) 025023, [arXiv:0809.3808]

    2009 arXiv

  29. [37]

    Kats and P

    Y. Kats and P. Petrov,Effect of curvature squared corrections in AdS on the viscosity of the dual gauge theory, JHEP 01 (2009) 044, [arXiv:0712.0743]

    2009 arXiv

  30. [38]

    Brigante, H

    M. Brigante, H. Liu, R. C. Myers, S. Shenker, and S. Yaida,Viscosity Bound Violation in Higher Derivative Gravity, Phys. Rev. D77 (2008) 126006, [arXiv:0712.0805]

    2008 arXiv

  31. [39]

    Brigante, H

    M. Brigante, H. Liu, R. C. Myers, S. Shenker, and S. Yaida,The Viscosity Bound and Causality Violation, Phys. Rev. Lett.100 (2008) 191601, [arXiv:0802.3318]

    2008 arXiv

  32. [40]

    Policastro, D

    G. Policastro, D. T. Son, and A. O. Starinets,The Shear viscosity of strongly coupled N=4 supersymmetric Yang-Mills plasma, Phys. Rev. Lett.87 (2001) 081601, [hep-th/0104066]

    2001 arXiv

  33. [41]

    Policastro, D

    G. Policastro, D. T. Son, and A. O. Starinets,From AdS / CFT correspondence to hydrodynamics, JHEP 09 (2002) 043, [hep-th/0205052]

    2002 arXiv

  34. [42]

    Simmons-Duffin,The Conformal Bootstrap, inTheoretical Advanced Study Institute in Elementary Particle Physics: New Frontiers in Fields and Strings, pp

    D. Simmons-Duffin,The Conformal Bootstrap, inTheoretical Advanced Study Institute in Elementary Particle Physics: New Frontiers in Fields and Strings, pp. 1–74, 2017.arXiv:1602.07982

    2017 arXiv

  35. [43]

    Penedones,TASI lectures on AdS/CFT., inTheoretical Advanced Study Institute in Elementary Particle Physics: New Frontiers in Fields and Strings, pp

    J. Penedones,TASI lectures on AdS/CFT., inTheoretical Advanced Study Institute in Elementary Particle Physics: New Frontiers in Fields and Strings, pp. 75–136, 2017.arXiv:1608.04948

    2017 arXiv

  36. [44]

    Zaffaroni,Introduction to the ads-cft correspondence, Classical and Quantum Gravity17 (2000), no

    A. Zaffaroni,Introduction to the ads-cft correspondence, Classical and Quantum Gravity17 (2000), no. 17 3571

    2000

  37. [45]

    Hartman,Lectures on quantum gravity and black holes, Cornell University 21 (2015)

    T. Hartman,Lectures on quantum gravity and black holes, Cornell University 21 (2015)

    2015

  38. [46]

    Karlsson, A

    R. Karlsson, A. Parnachev, and P. Tadić,Thermalization in large-N CFTs, JHEP 09 (2021) 205, [arXiv:2102.04953]

    2021 arXiv

  39. [47]

    El-Showk and K

    S. El-Showk and K. Papadodimas,Emergent Spacetime and Holographic CFTs, JHEP 10 (2012) 106, [arXiv:1101.4163]. 122

    2012 arXiv

  40. [48]

    Iliesiu, M

    L. Iliesiu, M. Koloğlu, R. Mahajan, E. Perlmutter, and D. Simmons-Duffin, The Conformal Bootstrap at Finite Temperature, JHEP 10 (2018) 070, [arXiv:1802.10266]

    2018 arXiv

  41. [49]

    F. A. Dolan and H. Osborn,Conformal four point functions and the operator product expansion, Nucl. Phys. B599 (2001) 459–496, [hep-th/0011040]

    2001 arXiv

  42. [50]

    F. A. Dolan and H. Osborn,Conformal partial waves and the operator product expansion, Nucl. Phys. B678 (2004) 491–507, [hep-th/0309180]

    2004 arXiv

  43. [51]

    M. S. Costa, J. Penedones, D. Poland, and S. Rychkov,Spinning Conformal Correlators, JHEP 11 (2011) 071, [arXiv:1107.3554]

    2011 arXiv

  44. [52]

    M. S. Costa, J. Penedones, D. Poland, and S. Rychkov,Spinning Conformal Blocks, JHEP 11 (2011) 154, [arXiv:1109.6321]

    2011 arXiv

  45. [53]

    Heemskerk, J

    I. Heemskerk, J. Penedones, J. Polchinski, and J. Sully,Holography from Conformal Field Theory, JHEP 10 (2009) 079, [arXiv:0907.0151]

    2009 arXiv

  46. [54]

    X. O. Camanho, J. D. Edelstein, J. Maldacena, and A. Zhiboedov,Causality Constraints on Corrections to the Graviton Three-Point Coupling, JHEP 02 (2016) 020, [arXiv:1407.5597]

    2016 arXiv

  47. [55]

    Keski-Vakkuri,Bulk and boundary dynamics in BTZ black holes, Phys

    E. Keski-Vakkuri,Bulk and boundary dynamics in BTZ black holes, Phys. Rev. D59 (1999) 104001, [hep-th/9808037]

    1999 arXiv

  48. [56]

    Karlsson, M

    R. Karlsson, M. Kulaxizi, A. Parnachev, and P. Tadić,Leading Multi-Stress Tensors and Conformal Bootstrap, JHEP 01 (2020) 076, [arXiv:1909.05775]

    2020 arXiv

  49. [57]

    Li,Heavy-light Bootstrap from Lorentzian Inversion Formula, JHEP 07 (2020) 046, [arXiv:1910.06357]

    Y.-Z. Li,Heavy-light Bootstrap from Lorentzian Inversion Formula, JHEP 07 (2020) 046, [arXiv:1910.06357]

    2020 arXiv

  50. [58]

    Li and H.-Y

    Y.-Z. Li and H.-Y. Zhang,More on heavy-light bootstrap up to double-stress-tensor, JHEP 10 (2020) 055, [arXiv:2004.04758]

    2020 arXiv

  51. [59]

    Karlsson, M

    R. Karlsson, M. Kulaxizi, A. Parnachev, and P. Tadić,Stress tensor sector of conformal correlators operators in the Regge limit, JHEP 07 (2020) 019, [arXiv:2002.12254]

    2020 arXiv

  52. [60]

    Dodelson and A

    M. Dodelson and A. Zhiboedov,Gravitational orbits, double-twist mirage, and many-body scars, JHEP 12 (2022) 163, [arXiv:2204.09749]

    2022 arXiv

  53. [61]

    Dodelson, A

    M. Dodelson, A. Grassi, C. Iossa, D. Panea Lichtig, and A. Zhiboedov, Holographic thermal correlators from supersymmetric instantons, SciPost Phys. 14 (2023) 116, [arXiv:2206.07720]

    2023 arXiv

  54. [62]

    Dodelson, C

    M. Dodelson, C. Iossa, R. Karlsson, and A. Zhiboedov,A thermal product formula, arXiv:2304.12339

    arXiv

  55. [63]

    E. Katz, S. Sachdev, E. S. Sørensen, and W. Witczak-Krempa,Conformal field theories at nonzero temperature: Operator product expansions, Monte Carlo, and holography, Phys. Rev. B90 (2014), no. 24 245109, [arXiv:1409.3841]. 123

    2014 arXiv

  56. [64]

    Manenti,Thermal CFTs in momentum space, JHEP 01 (2020) 009, [arXiv:1905.01355]

    A. Manenti,Thermal CFTs in momentum space, JHEP 01 (2020) 009, [arXiv:1905.01355]

    2020 arXiv

  57. [65]

    Kulaxizi, G

    M. Kulaxizi, G. S. Ng, and A. Parnachev,Subleading Eikonal, AdS/CFT and Double Stress Tensors, JHEP 10 (2019) 107, [arXiv:1907.00867]

    2019 arXiv

  58. [66]

    Karlsson, M

    R. Karlsson, M. Kulaxizi, A. Parnachev, and P. Tadić,Black Holes and Conformal Regge Bootstrap, JHEP 10 (2019) 046, [arXiv:1904.00060]

    2019 arXiv

  59. [67]

    Karlsson,Multi-stress tensors and next-to-leading singularities in the Regge limit, JHEP 08 (2020) 037, [arXiv:1912.01577]

    R. Karlsson,Multi-stress tensors and next-to-leading singularities in the Regge limit, JHEP 08 (2020) 037, [arXiv:1912.01577]

    2020 arXiv

  60. [68]

    Parnachev and K

    A. Parnachev and K. Sen,Notes on AdS-Schwarzschild eikonal phase, JHEP 03 (2021) 289, [arXiv:2011.06920]

    2021 arXiv

  61. [69]

    Parnachev,Near Lightcone Thermal Conformal Correlators and Holography, J

    A. Parnachev,Near Lightcone Thermal Conformal Correlators and Holography, J. Phys. A54 (2021), no. 15 155401, [arXiv:2005.06877]

    2021 arXiv

  62. [70]

    J. M. Maldacena,Eternal black holes in anti-de Sitter, JHEP 04 (2003) 021, [hep-th/0106112]

    2003 arXiv

  63. [71]

    Kubo,Statistical mechanical theory of irreversible processes

    R. Kubo,Statistical mechanical theory of irreversible processes. 1. General theory and simple applications in magnetic and conduction problems, J. Phys. Soc. Jap.12 (1957) 570–586

    1957

  64. [72]

    P. C. Martin and J. S. Schwinger,Theory of many particle systems. 1., Phys. Rev.115 (1959) 1342–1373

    1959

  65. [73]

    A. L. Fitzpatrick, J. Kaplan, M. T. Walters, and J. Wang,Hawking from Catalan, JHEP 05 (2016) 069, [arXiv:1510.00014]

    2016 arXiv

  66. [74]

    Festuccia,Black hole singularities in the framework of gauge/string duality

    G. Festuccia,Black hole singularities in the framework of gauge/string duality. PhD thesis, Massachusetts Institute of Technology, 2007

    2007

  67. [75]

    L. F. Alday, M. Kologlu, and A. Zhiboedov,Holographic correlators at finite temperature, JHEP 06 (2021) 082, [arXiv:2009.10062]

    2021 arXiv

  68. [76]

    A. L. Fitzpatrick, J. Kaplan, and M. T. Walters,Universality of Long-Distance AdS Physics from the CFT Bootstrap, JHEP 08 (2014) 145, [arXiv:1403.6829]

    2014 arXiv

  69. [77]

    Komargodski and A

    Z. Komargodski and A. Zhiboedov,Convexity and Liberation at Large Spin, JHEP 11 (2013) 140, [arXiv:1212.4103]

    2013 arXiv

  70. [78]

    Marchetto, A

    E. Marchetto, A. Miscioscia, and E. Pomoni,Sum rules & Tauberian theorems at finite temperature, arXiv:2312.13030

    arXiv

  71. [79]

    Chapman, D

    S. Chapman, D. A. Galante, E. Harris, S. U. Sheorey, and D. Vegh,Complex geodesics in de Sitter space, JHEP 03 (2023) 006, [arXiv:2212.01398]

    2023 arXiv

  72. [80]

    Aalsma, M

    L. Aalsma, M. M. Faruk, J. P. van der Schaar, M. R. Visser, and J. de Witte,Late-time correlators and complex geodesics in de Sitter space, SciPost Phys.15 (2023), no. 1 031, [arXiv:2212.01394]. 124

    2023 arXiv

  73. [81]

    Hamilton, D

    A. Hamilton, D. N. Kabat, G. Lifschytz, and D. A. Lowe,Local bulk operators in AdS/CFT: A Holographic description of the black hole interior, Phys. Rev.D75 (2007) 106001, [hep-th/0612053]. [Erratum: Phys. Rev.D75,129902(2007)]

    2007 arXiv

  74. [82]

    Koshelev and A

    A. Koshelev and A. Tokareva,Non-perturbative quantum gravity denounces singular Black Holes, arXiv:2404.07925

    arXiv

  75. [83]

    A. L. Fitzpatrick, K.-W. Huang, D. Meltzer, E. Perlmutter, and D. Simmons-Duffin,Model-dependence of minimal-twist OPEs in d> 2 holographic CFTs, JHEP 11 (2020) 060, [arXiv:2007.07382]

    2020 arXiv

  76. [84]

    Frenkel, S

    A. Frenkel, S. A. Hartnoll, J. Kruthoff, and Z. D. Shi,Holographic flows from CFT to the Kasner universe, JHEP 08 (2020) 003, [arXiv:2004.01192]

    2020 arXiv

  77. [85]

    V. A. Belinsky, I. M. Khalatnikov, and E. M. Lifshitz,Oscillatory approach to a singular point in the relativistic cosmology, Adv. Phys.19 (1970) 525–573

    1970

  78. [86]

    C. W. Misner,Mixmaster universe, Phys. Rev. Lett.22 (1969) 1071–1074

    1969

  79. [87]

    De Clerck, S

    M. De Clerck, S. A. Hartnoll, and J. E. Santos,Mixmaster chaos in an AdS black hole interior, arXiv:2312.11622

    arXiv

  80. [88]

    L. D. Landau and E. M. Lifshitz,Fluid Mechanics, 2nd ed.(Pergamon Press, New York, 1987), 2 ed., 1987

    1987

  81. [89]

    Meltzer and E

    D. Meltzer and E. Perlmutter,Beyond a =c: gravitational couplings to matter and the stress tensor OPE, JHEP 07 (2018) 157, [arXiv:1712.04861]

    2018 arXiv

  82. [90]

    Afkhami-Jeddi, S

    N. Afkhami-Jeddi, S. Kundu, and A. Tajdini,A Conformal Collider for Holographic CFTs, JHEP 10 (2018) 156, [arXiv:1805.07393]

    2018 arXiv

  83. [91]

    A. L. Fitzpatrick, J. Kaplan, and M. T. Walters,Virasoro Conformal Blocks and Thermality from Classical Background Fields, JHEP 11 (2015) 200, [arXiv:1501.05315]

    2015 arXiv

  84. [92]

    Kulaxizi, G

    M. Kulaxizi, G. S. Ng, and A. Parnachev,Black Holes, Heavy States, Phase Shift and Anomalous Dimensions, SciPost Phys.6 (2019), no. 6 065, [arXiv:1812.03120]

    2019 arXiv

  85. [93]

    Karlsson, M

    R. Karlsson, M. Kulaxizi, G. S. Ng, A. Parnachev, and P. Tadić,CFT correlators,W-algebras and generalized Catalan numbers, JHEP 06 (2022) 162, [arXiv:2111.07924]

    2022 arXiv

  86. [94]

    Li, Z.-F

    Y.-Z. Li, Z.-F. Mai, and H. Lü,Holographic OPE Coefficients from AdS Black Holes with Matters, JHEP 09 (2019) 001, [arXiv:1905.09302]

    2019 arXiv

  87. [95]

    Huang,Stress-tensor commutators in conformal field theories near the lightcone, Phys

    K.-W. Huang,Stress-tensor commutators in conformal field theories near the lightcone, Phys. Rev. D100 (2019), no. 6 061701, [arXiv:1907.00599]

    2019 arXiv

  88. [96]

    A. L. Fitzpatrick, K.-W. Huang, and D. Li,Probing universalities in d> 2 CFTs: from black holes to shockwaves, JHEP 11 (2019) 139, [arXiv:1907.10810]. 125

    2019 arXiv

  89. [97]

    Huang,Lightcone Commutator and Stress-Tensor Exchange ind> 2 CFTs, Phys

    K.-W. Huang,Lightcone Commutator and Stress-Tensor Exchange ind> 2 CFTs, Phys. Rev. D102 (2020), no. 2 021701, [arXiv:2002.00110]

    2020 arXiv

  90. [98]

    Huang,d> 2 stress-tensor operator product expansion near a line, Phys

    K.-W. Huang,d> 2 stress-tensor operator product expansion near a line, Phys. Rev. D103 (2021), no. 12 121702, [arXiv:2103.09930]

    2021 arXiv

  91. [99]

    Rodriguez-Gomez and J

    D. Rodriguez-Gomez and J. G. Russo,Thermal correlation functions in CFT and factorization, JHEP 11 (2021) 049, [arXiv:2105.13909]

    2021 arXiv

  92. [100]

    Krishna and D

    H. Krishna and D. Rodriguez-Gomez,Holographic thermal correlators revisited, JHEP 11 (2021) 139, [arXiv:2108.00277]

    2021 arXiv

  93. [101]

    Huang,Approximate symmetries in d = 4 CFTs with an Einstein gravity dual, JHEP 09 (2022) 053, [arXiv:2202.09998]

    K.-W. Huang,Approximate symmetries in d = 4 CFTs with an Einstein gravity dual, JHEP 09 (2022) 053, [arXiv:2202.09998]

    2022 arXiv

  94. [102]

    P. Basu, D. Das, S. Datta, and S. Pal,Thermality of eigenstates in conformal field theories, Phys. Rev. E96 (2017), no. 2 022149, [arXiv:1705.03001]

    2017 arXiv

  95. [103]

    He, F.-L

    S. He, F.-L. Lin, and J.-j. Zhang,Dissimilarities of reduced density matrices and eigenstate thermalization hypothesis, JHEP 12 (2017) 073, [arXiv:1708.05090]

    2017 arXiv

  96. [104]

    Datta, P

    S. Datta, P. Kraus, and B. Michel,Typicality and thermality in 2d CFT, JHEP 07 (2019) 143, [arXiv:1904.00668]

    2019 arXiv

  97. [105]

    P. K. Kovtun and A. O. Starinets,Quasinormal modes and holography, Phys. Rev. D72 (2005) 086009, [hep-th/0506184]

    2005 arXiv

  98. [106]

    Kovtun and A

    P. Kovtun and A. Starinets,Thermal spectral functions of strongly coupled N=4 supersymmetric Yang-Mills theory, Phys. Rev. Lett.96 (2006) 131601, [hep-th/0602059]

    2006 arXiv

  99. [107]

    Liu and A

    H. Liu and A. A. Tseytlin,D = 4 superYang-Mills, D = 5 gauged supergravity, and D = 4 conformal supergravity, Nucl. Phys. B533 (1998) 88–108, [hep-th/9804083]

    1998 arXiv

  100. [108]

    Skenderis,Lecture notes on holographic renormalization, Class

    K. Skenderis,Lecture notes on holographic renormalization, Class. Quant. Grav.19 (2002) 5849–5876, [hep-th/0209067]

    2002 arXiv

  101. [109]

    Lashkari, A

    N. Lashkari, A. Dymarsky, and H. Liu,Eigenstate Thermalization Hypothesis in Conformal Field Theory, J. Stat. Mech.1803 (2018), no. 3 033101, [arXiv:1610.00302]

    2018 arXiv

  102. [110]

    Lashkari, A

    N. Lashkari, A. Dymarsky, and H. Liu,Universality of Quantum Information in Chaotic CFTs, JHEP 03 (2018) 070, [arXiv:1710.10458]

    2018 arXiv

  103. [111]

    Osborn and A

    H. Osborn and A. C. Petkou,Implications of conformal invariance in field theories for general dimensions, Annals Phys.231 (1994) 311–362, [hep-th/9307010]

    1994 arXiv

  104. [112]

    D. M. Hofman and J. Maldacena,Conformal collider physics: Energy and charge correlations, JHEP 05 (2008) 012, [arXiv:0803.1467]. 126

    2008 arXiv

  105. [113]

    D. M. Hofman,Higher Derivative Gravity, Causality and Positivity of Energy in a UV complete QFT, Nucl. Phys. B823 (2009) 174–194, [arXiv:0907.1625]

    2009 arXiv

  106. [114]

    Kulaxizi and A

    M. Kulaxizi and A. Parnachev,Energy Flux Positivity and Unitarity in CFTs, Phys. Rev. Lett.106 (2011) 011601, [arXiv:1007.0553]

    2011 arXiv

  107. [115]

    Hartman, S

    T. Hartman, S. Jain, and S. Kundu,Causality Constraints in Conformal Field Theory, JHEP 05 (2016) 099, [arXiv:1509.00014]

    2016 arXiv

  108. [116]

    D. Li, D. Meltzer, and D. Poland,Conformal Collider Physics from the Lightcone Bootstrap, JHEP 02 (2016) 143, [arXiv:1511.08025]

    2016 arXiv

  109. [117]

    Komargodski, M

    Z. Komargodski, M. Kulaxizi, A. Parnachev, and A. Zhiboedov,Conformal Field Theories and Deep Inelastic Scattering, Phys. Rev. D95 (2017), no. 6 065011, [arXiv:1601.05453]

    2017 arXiv

  110. [118]

    Hartman, S

    T. Hartman, S. Jain, and S. Kundu,A New Spin on Causality Constraints, JHEP 10 (2016) 141, [arXiv:1601.07904]

    2016 arXiv

  111. [119]

    D. M. Hofman, D. Li, D. Meltzer, D. Poland, and F. Rejon-Barrera,A Proof of the Conformal Collider Bounds, JHEP 06 (2016) 111, [arXiv:1603.03771]

    2016 arXiv

  112. [120]

    Faulkner, R

    T. Faulkner, R. G. Leigh, O. Parrikar, and H. Wang,Modular Hamiltonians for Deformed Half-Spaces and the Averaged Null Energy Condition, JHEP 09 (2016) 038, [arXiv:1605.08072]

    2016 arXiv

  113. [121]

    Hartman, S

    T. Hartman, S. Kundu, and A. Tajdini,Averaged Null Energy Condition from Causality, JHEP 07 (2017) 066, [arXiv:1610.05308]

    2017 arXiv

  114. [122]

    Rastelli and X

    L. Rastelli and X. Zhou,Mellin amplitudes forAdS5×S5, Phys. Rev. Lett. 118 (2017), no. 9 091602, [arXiv:1608.06624]

    2017 arXiv

  115. [123]

    L. F. Alday and A. Bissi,Loop Corrections to Supergravity onAdS5×S5, Phys. Rev. Lett.119 (2017), no. 17 171601, [arXiv:1706.02388]

    2017 arXiv

  116. [124]

    Aprile, J

    F. Aprile, J. M. Drummond, P. Heslop, and H. Paul,Quantum Gravity from Conformal Field Theory, JHEP 01 (2018) 035, [arXiv:1706.02822]

    2018 arXiv

  117. [125]

    Rastelli and X

    L. Rastelli and X. Zhou,How to Succeed at Holographic Correlators Without Really Trying, JHEP 04 (2018) 014, [arXiv:1710.05923]

    2018 arXiv

  118. [126]

    Withers,Short-lived modes from hydrodynamic dispersion relations, JHEP 06 (2018) 059, [arXiv:1803.08058]

    B. Withers,Short-lived modes from hydrodynamic dispersion relations, JHEP 06 (2018) 059, [arXiv:1803.08058]

    2018 arXiv

  119. [127]

    Grozdanov, P

    S. Grozdanov, P. K. Kovtun, A. O. Starinets, and P. Tadić,Convergence of the Gradient Expansion in Hydrodynamics, Phys. Rev. Lett.122 (2019), no. 25 251601, [arXiv:1904.01018]

    2019 arXiv

  120. [128]

    Grozdanov, P

    S. Grozdanov, P. K. Kovtun, A. O. Starinets, and P. Tadić,The complex life of hydrodynamic modes, JHEP 11 (2019) 097, [arXiv:1904.12862]. 127

    2019 arXiv

  121. [129]

    Abbasi and S

    N. Abbasi and S. Tahery,Complexified quasinormal modes and the pole-skipping in a holographic system at finite chemical potential, JHEP 10 (2020) 076, [arXiv:2007.10024]

    2020 arXiv

  122. [130]

    Jansen and C

    A. Jansen and C. Pantelidou,Quasinormal modes in charged fluids at complex momentum, JHEP 10 (2020) 121, [arXiv:2007.14418]

    2020 arXiv

  123. [131]

    Grozdanov,Bounds on transport from univalence and pole-skipping, Phys

    S. Grozdanov,Bounds on transport from univalence and pole-skipping, Phys. Rev. Lett.126 (2021), no. 5 051601, [arXiv:2008.00888]

    2021 arXiv

  124. [132]

    C. Choi, M. Mezei, and G. Sárosi,Pole skipping away from maximal chaos, arXiv:2010.08558

    2010 arXiv

  125. [133]

    Baggioli,How small hydrodynamics can go, Phys

    M. Baggioli,How small hydrodynamics can go, Phys. Rev. D103 (2021), no. 8 086001, [arXiv:2010.05916]

    2021 arXiv

  126. [134]

    Grozdanov, A

    S. Grozdanov, A. O. Starinets, and P. Tadić,Hydrodynamic dispersion relations at finite coupling, JHEP 06 (2021) 180, [arXiv:2104.11035]

    2021 arXiv

  127. [135]

    Caron-Huot,Asymptotics of thermal spectral functions, Phys

    S. Caron-Huot,Asymptotics of thermal spectral functions, Phys. Rev. D79 (2009) 125009, [arXiv:0903.3958]

    2009 arXiv

  128. [136]

    Gobeil, A

    Y. Gobeil, A. Maloney, G. S. Ng, and J.-q. Wu,Thermal Conformal Blocks, SciPost Phys.7 (2019), no. 2 015, [arXiv:1802.10537]

    2019 arXiv

  129. [137]

    L. V. Delacrétaz, T. Hartman, S. A. Hartnoll, and A. Lewkowycz, Thermalization, Viscosity and the Averaged Null Energy Condition, JHEP 10 (2018) 028, [arXiv:1805.04194]

    2018 arXiv

  130. [138]

    L. V. Delacretaz,Heavy Operators and Hydrodynamic Tails, SciPost Phys.9 (2020), no. 3 034, [arXiv:2006.01139]

    2020 arXiv

  131. [139]

    L. V. Delacretaz, A. L. Fitzpatrick, E. Katz, and M. T. Walters, Thermalization and Hydrodynamics of Two-Dimensional Quantum Field Theories, SciPost Phys.12 (2022) 119, [arXiv:2105.02229]

    2022 arXiv

  132. [140]

    Barrat, E

    J. Barrat, E. Marchetto, A. Miscioscia, and E. Pomoni,The thermal bootstrap for the critical O(N) model, arXiv:2411.00978

    arXiv

  133. [141]

    Rychkov,EPFL Lectures on Conformal Field Theory in D>= 3 Dimensions, arXiv:1601.05000

    S. Rychkov,EPFL Lectures on Conformal Field Theory in D>= 3 Dimensions, arXiv:1601.05000

    arXiv

  134. [142]

    Poland, S

    D. Poland, S. Rychkov, and A. Vichi,The Conformal Bootstrap: Theory, Numerical Techniques, and Applications, Rev. Mod. Phys.91 (2019) 015002, [arXiv:1805.04405]

    2019 arXiv

  135. [143]

    Córdova, J

    C. Córdova, J. Maldacena, and G. J. Turiaci,Bounds on OPE Coefficients from Interference Effects in the Conformal Collider, JHEP 11 (2017) 032, [arXiv:1710.03199]

    2017 arXiv

  136. [144]

    Meltzer,Higher Spin ANEC and the Space of CFTs, JHEP 07 (2019) 001, [arXiv:1811.01913]

    D. Meltzer,Higher Spin ANEC and the Space of CFTs, JHEP 07 (2019) 001, [arXiv:1811.01913]. 128

    2019 arXiv

  137. [145]

    Balakrishnan, T

    S. Balakrishnan, T. Faulkner, Z. U. Khandker, and H. Wang,A General Proof of the Quantum Null Energy Condition, JHEP 09 (2019) 020, [arXiv:1706.09432]

    2019 arXiv

  138. [146]

    Córdova and K

    C. Córdova and K. Diab,Universal Bounds on Operator Dimensions from the Average Null Energy Condition, JHEP 02 (2018) 131, [arXiv:1712.01089]

    2018 arXiv

  139. [147]

    Kravchuk and D

    P. Kravchuk and D. Simmons-Duffin,Light-ray operators in conformal field theory, JHEP 11 (2018) 102, [arXiv:1805.00098]

    2018 arXiv

  140. [148]

    Córdova and S.-H

    C. Córdova and S.-H. Shao,Light-ray Operators and the BMS Algebra, Phys. Rev. D98 (2018), no. 12 125015, [arXiv:1810.05706]

    2018 arXiv

  141. [149]

    Ceyhan and T

    F. Ceyhan and T. Faulkner,Recovering the QNEC from the ANEC, Commun. Math. Phys.377 (2020), no. 2 999–1045, [arXiv:1812.04683]

    2020 arXiv

  142. [150]

    Belin, D

    A. Belin, D. M. Hofman, and G. Mathys,Einstein gravity from ANEC correlators, JHEP 08 (2019) 032, [arXiv:1904.05892]

    2019 arXiv

  143. [151]

    Kologlu, P

    M. Kologlu, P. Kravchuk, D. Simmons-Duffin, and A. Zhiboedov,The light-ray OPE and conformal colliders, JHEP 01 (2021) 128, [arXiv:1905.01311]

    2021 arXiv

  144. [152]

    Manenti, A

    A. Manenti, A. Stergiou, and A. Vichi,Implications of ANEC for SCFTs in four dimensions, JHEP 01 (2020) 093, [arXiv:1905.09293]

    2020 arXiv

  145. [153]

    Belin, D

    A. Belin, D. M. Hofman, G. Mathys, and M. T. Walters,On the stress tensor light-ray operator algebra, JHEP 05 (2021) 033, [arXiv:2011.13862]

    2021 arXiv

  146. [154]

    Beşken, J

    M. Beşken, J. De Boer, and G. Mathys,On local and integrated stress-tensor commutators, JHEP 21 (2020) 148, [arXiv:2012.15724]

    2020 arXiv

  147. [155]

    G. P. Korchemsky, E. Sokatchev, and A. Zhiboedov,Generalizing event shapes: in search of lost collider time, JHEP 08 (2022) 188, [arXiv:2106.14899]

    2022 arXiv

  148. [156]

    G. P. Korchemsky and A. Zhiboedov,On the light-ray algebra in conformal field theories, JHEP 02 (2022) 140, [arXiv:2109.13269]

    2022 arXiv

  149. [157]

    Caron-Huot, M

    S. Caron-Huot, M. Kologlu, P. Kravchuk, D. Meltzer, and D. Simmons-Duffin,Detectors in weakly-coupled field theories, arXiv:2209.00008

    arXiv

  150. [158]

    de Boer, M

    J. de Boer, M. Kulaxizi, and A. Parnachev,AdS(7)/CFT(6), Gauss-Bonnet Gravity, and Viscosity Bound, JHEP 03 (2010) 087, [arXiv:0910.5347]

    2010 arXiv

  151. [159]

    X. O. Camanho and J. D. Edelstein,Causality constraints in AdS/CFT from conformal collider physics and Gauss-Bonnet gravity, JHEP 04 (2010) 007, [arXiv:0911.3160]

    2010 arXiv

  152. [160]

    Buchel, J

    A. Buchel, J. Escobedo, R. C. Myers, M. F. Paulos, A. Sinha, and M. Smolkin,Holographic GB gravity in arbitrary dimensions, JHEP 03 (2010) 111, [arXiv:0911.4257]. 129

    2010 arXiv

  153. [161]

    Buchel and R

    A. Buchel and R. C. Myers,Causality of Holographic Hydrodynamics, JHEP 08 (2009) 016, [arXiv:0906.2922]

    2009 arXiv

  154. [162]

    Buchel and S

    A. Buchel and S. Cremonini,Viscosity Bound and Causality in Superfluid Plasma, JHEP 10 (2010) 026, [arXiv:1007.2963]

    2010 arXiv

  155. [163]

    Cai, Z.-Y

    R.-G. Cai, Z.-Y. Nie, and H.-Q. Zhang,Holographic p-wave superconductors from Gauss-Bonnet gravity, Phys. Rev. D82 (2010) 066007, [arXiv:1007.3321]

    2010 arXiv

  156. [164]

    Y. Bu, M. Lublinsky, and A. Sharon,Hydrodynamics dual to Einstein-Gauss-Bonnet gravity: all-order gradient resummation, JHEP 06 (2015) 162, [arXiv:1504.01370]

    2015 arXiv

  157. [165]

    Grozdanov, N

    S. Grozdanov, N. Kaplis, and A. O. Starinets,From strong to weak coupling in holographic models of thermalization, JHEP 07 (2016) 151, [arXiv:1605.02173]

    2016 arXiv

  158. [166]

    Andrade, E

    T. Andrade, E. Caceres, and C. Keeler,Boundary causality versus hyperbolicity for spherical black holes in Gauss–Bonnet gravity, Class. Quant. Grav.34 (2017), no. 13 135003, [arXiv:1610.06078]

    2017 arXiv

  159. [167]

    Grozdanov and W

    S. Grozdanov and W. van der Schee,Coupling Constant Corrections in a Holographic Model of Heavy Ion Collisions, Phys. Rev. Lett.119 (2017), no. 1 011601, [arXiv:1610.08976]

    2017 arXiv

  160. [168]

    Andrade, J

    T. Andrade, J. Casalderrey-Solana, and A. Ficnar,Holographic Isotropisation in Gauss-Bonnet Gravity, JHEP 02 (2017) 016, [arXiv:1610.08987]

    2017 arXiv

  161. [169]

    Grozdanov and A

    S. Grozdanov and A. O. Starinets,Second-order transport, quasinormal modes and zero-viscosity limit in the Gauss-Bonnet holographic fluid, JHEP 03 (2017) 166, [arXiv:1611.07053]

    2017 arXiv

  162. [170]

    Chen, P.-C

    B. Chen, P.-C. Li, Y. Tian, and C.-Y. Zhang,Holographic Turbulence in Einstein-Gauss-Bonnet Gravity at LargeD, JHEP 01 (2019) 156, [arXiv:1804.05182]

    2019 arXiv

  163. [171]

    An, R.-G

    Y.-S. An, R.-G. Cai, and Y. Peng,Time Dependence of Holographic Complexity in Gauss-Bonnet Gravity, Phys. Rev. D98 (2018), no. 10 106013, [arXiv:1805.07775]

    2018 arXiv

  164. [172]

    Kulaxizi, A

    M. Kulaxizi, A. Parnachev, and A. Zhiboedov,Bulk Phase Shift, CFT Regge Limit and Einstein Gravity, JHEP 06 (2018) 121, [arXiv:1705.02934]

    2018 arXiv

  165. [173]

    D. Li, D. Meltzer, and D. Poland,Conformal Bootstrap in the Regge Limit, JHEP 12 (2017) 013, [arXiv:1705.03453]

    2017 arXiv

  166. [174]

    M. S. Costa, T. Hansen, and J. Penedones,Bounds for OPE coefficients on the Regge trajectory, JHEP 10 (2017) 197, [arXiv:1707.07689]

    2017 arXiv

  167. [175]

    Bonifacio, K

    J. Bonifacio, K. Hinterbichler, A. Joyce, and R. A. Rosen,Massive and Massless Spin-2 Scattering and Asymptotic Superluminality, JHEP 06 (2018) 075, [arXiv:1712.10020]. 130

    2018 arXiv

  168. [176]

    Kologlu, P

    M. Kologlu, P. Kravchuk, D. Simmons-Duffin, and A. Zhiboedov,Shocks, Superconvergence, and a Stringy Equivalence Principle, JHEP 11 (2020) 096, [arXiv:1904.05905]

    2020 arXiv

  169. [177]

    Caron-Huot, D

    S. Caron-Huot, D. Mazac, L. Rastelli, and D. Simmons-Duffin,AdS bulk locality from sharp CFT bounds, JHEP 11 (2021) 164, [arXiv:2106.10274]

    2021 arXiv

  170. [178]

    Zhiboedov,On Conformal Field Theories With Extremal a/c Values, JHEP 04 (2014) 038, [arXiv:1304.6075]

    A. Zhiboedov,On Conformal Field Theories With Extremal a/c Values, JHEP 04 (2014) 038, [arXiv:1304.6075]

    2014 arXiv

  171. [179]

    D. G. Boulware and S. Deser,String Generated Gravity Models, Phys. Rev. Lett.55 (1985) 2656

    1985

  172. [180]

    Cai,Gauss-Bonnet black holes in AdS spaces, Phys

    R.-G. Cai,Gauss-Bonnet black holes in AdS spaces, Phys. Rev. D65 (2002) 084014, [hep-th/0109133]

    2002 arXiv

  173. [181]

    H. B. Meyer,Transport Properties of the Quark-Gluon Plasma: A Lattice QCD Perspective, Eur. Phys. J. A47 (2011) 86, [arXiv:1104.3708]

    2011 arXiv

  174. [182]

    F. M. Haehl, W. Reeves, and M. Rozali,Reparametrization modes, shadow operators, and quantum chaos in higher-dimensional CFTs, JHEP 11 (2019) 102, [arXiv:1909.05847]

    2019 arXiv

  175. [183]

    Berenstein, Z

    D. Berenstein, Z. Li, and J. Simon,ISCOs in AdS/CFT, Class. Quant. Grav. 38 (2021), no. 4 045009, [arXiv:2009.04500]

    2021 arXiv

  176. [184]

    Bianchi and G

    M. Bianchi and G. Di Russo,Turning black holes and D-branes inside out of their photon spheres, Phys. Rev. D105 (2022), no. 12 126007, [arXiv:2110.09579]

    2022 arXiv

  177. [185]

    Parisini, K

    E. Parisini, K. Skenderis, and B. Withers,Embedding formalism for CFTs in general states on curved backgrounds, Phys. Rev. D107 (2023), no. 6 066022, [arXiv:2209.09250]

    2023 arXiv

  178. [186]

    A. B. Zamolodchikov,Infinite additional symmetries in two-dimensional conformal quantum field theory, Theoretical and Mathematical Physics65 (1985)

    1985

  179. [187]

    Lovelock,The Einstein tensor and its generalizations, J

    D. Lovelock,The Einstein tensor and its generalizations, J. Math. Phys.12 (1971) 498–501

    1971

  180. [188]

    R. C. Myers and B. Robinson,Black Holes in Quasi-topological Gravity, JHEP 08 (2010) 067, [arXiv:1003.5357]

    2010 arXiv

  181. [189]

    R. C. Myers, M. F. Paulos, and A. Sinha,Holographic studies of quasi-topological gravity, JHEP 08 (2010) 035, [arXiv:1004.2055]

    2010 arXiv

  182. [190]

    Bhatta and T

    A. Bhatta and T. Mandal,Exact thermal correlators of holographic CFTs, JHEP 02 (2023) 222, [arXiv:2211.02449]

    2023 arXiv

  183. [191]

    Bajc and A

    B. Bajc and A. R. Lugo,Holographic thermal propagator for arbitrary scale dimensions, JHEP 05 (2023) 103, [arXiv:2212.13639]. 131

    2023 arXiv

  184. [192]

    C. T. Asplund, A. Bernamonti, F. Galli, and T. Hartman,Holographic Entanglement Entropy from 2d CFT: Heavy States and Local Quenches, JHEP 02 (2015) 171, [arXiv:1410.1392]

    2015 arXiv

  185. [193]

    Hijano, P

    E. Hijano, P. Kraus, E. Perlmutter, and R. Snively,Semiclassical Virasoro blocks from AdS3 gravity, JHEP 12 (2015) 077, [arXiv:1508.04987]

    2015 arXiv

  186. [194]

    Galliani, S

    A. Galliani, S. Giusto, E. Moscato, and R. Russo,Correlators at large c without information loss, JHEP 09 (2016) 065, [arXiv:1606.01119]

    2016 arXiv

  187. [195]

    Balasubramanian, A

    V. Balasubramanian, A. Bernamonti, B. Craps, T. De Jonckheere, and F. Galli,Heavy-Heavy-Light-Light correlators in Liouville theory, JHEP 08 (2017) 045, [arXiv:1705.08004]

    2017 arXiv

  188. [196]

    Galliani, S

    A. Galliani, S. Giusto, and R. Russo,Holographic 4-point correlators with heavy states, JHEP 10 (2017) 040, [arXiv:1705.09250]

    2017 arXiv

  189. [197]

    Faulkner and H

    T. Faulkner and H. Wang,Probing beyond ETH at largec, JHEP 06 (2018) 123, [arXiv:1712.03464]

    2018 arXiv

  190. [198]

    Giusto, R

    S. Giusto, R. Russo, and C. Wen,Holographic correlators in AdS3, JHEP 03 (2019) 096, [arXiv:1812.06479]

    2019 arXiv

  191. [199]

    Giusto, R

    S. Giusto, R. Russo, A. Tyukov, and C. Wen,Holographic correlators in AdS3 without Witten diagrams, JHEP 09 (2019) 030, [arXiv:1905.12314]

    2019 arXiv

  192. [200]

    Giusto, M

    S. Giusto, M. R. R. Hughes, and R. Russo,The Regge limit of AdS3 holographic correlators, JHEP 11 (2020) 018, [arXiv:2007.12118]

    2020 arXiv

  193. [201]

    Ceplak and M

    N. Ceplak and M. R. R. Hughes,The Regge limit of AdS3 holographic correlators with heavy states: towards the black hole regime, JHEP 07 (2021) 021, [arXiv:2102.09549]

    2021 arXiv

  194. [202]

    Bufalini, S

    D. Bufalini, S. Iguri, N. Kovensky, and D. Turton,Worldsheet Correlators in Black Hole Microstates, Phys. Rev. Lett.129 (2022), no. 12 121603, [arXiv:2203.13828]

    2022 arXiv

  195. [203]

    Berenstein, D

    D. Berenstein, D. Grabovsky, and Z. Li,Aspects of holography in conical AdS3, JHEP 04 (2023) 029, [arXiv:2205.02256]

    2023 arXiv

  196. [204]

    Casalderrey-Solana, N

    J. Casalderrey-Solana, N. I. Gushterov, and B. Meiring,Resurgence and Hydrodynamic Attractors in Gauss-Bonnet Holography, JHEP 04 (2018) 042, [arXiv:1712.02772]

    2018 arXiv

  197. [205]

    D. T. Son and A. O. Starinets,Minkowski space correlators in AdS / CFT correspondence: Recipe and applications, JHEP 09 (2002) 042, [hep-th/0205051]

    2002 arXiv

  198. [206]

    Policastro, D

    G. Policastro, D. T. Son, and A. O. Starinets,From AdS / CFT correspondence to hydrodynamics. 2. Sound waves, JHEP 12 (2002) 054, [hep-th/0210220]

    2002 arXiv

  199. [207]

    Romatschke and D

    P. Romatschke and D. T. Son,Spectral sum rules for the quark-gluon plasma, Physical Review D80 (sep, 2009) [arXiv:0903.3946]. 132

    2009 arXiv

  200. [208]

    F. M. Haehl and M. Rozali,Effective Field Theory for Chaotic CFTs, JHEP 10 (2018) 118, [arXiv:1808.02898]

    2018 arXiv

  201. [209]

    Jensen,Scrambling in nearly thermalized states at large central charge, arXiv:1906.05852

    K. Jensen,Scrambling in nearly thermalized states at large central charge, arXiv:1906.05852

    1906 arXiv

  202. [210]

    D. M. Ramirez,Chaos and pole skipping in CFT2, JHEP 12 (2021) 006, [arXiv:2009.00500]

    2021 arXiv

  203. [211]

    Festuccia and H

    G. Festuccia and H. Liu,A Bohr-Sommerfeld quantization formula for quasinormal frequencies of AdS black holes, Adv. Sci. Lett.2 (2009) 221–235, [arXiv:0811.1033]

    2009 arXiv

  204. [212]

    Caron-Huot,Analyticity in Spin in Conformal Theories, JHEP 09 (2017) 078, [arXiv:1703.00278]

    S. Caron-Huot,Analyticity in Spin in Conformal Theories, JHEP 09 (2017) 078, [arXiv:1703.00278]

    2017 arXiv

  205. [213]

    Simmons-Duffin, D

    D. Simmons-Duffin, D. Stanford, and E. Witten,A spacetime derivation of the Lorentzian OPE inversion formula, JHEP 07 (2018) 085, [arXiv:1711.03816]

    2018 arXiv

  206. [214]

    A. C. Petkou and A. Stergiou,Dynamics of Finite-Temperature Conformal Field Theories from Operator Product Expansion Inversion Formulas, Phys. Rev. Lett.121 (2018), no. 7 071602, [arXiv:1806.02340]

    2018 arXiv

  207. [215]

    Engelsöy and B

    J. Engelsöy and B. Sundborg,Tidal excitation as mixing in thermal CFT, JHEP 08 (2021) 085, [arXiv:2106.06520]

    2021 arXiv

  208. [216]

    Avdoshkin, A

    A. Avdoshkin, A. Dymarsky, and M. Smolkin,Krylov complexity in quantum field theory, and beyond, arXiv:2212.14429

    arXiv

  209. [217]

    Fortin, W.-J

    J.-F. Fortin, W.-J. Ma, V. Prilepina, and W. Skiba,Conformal Bootstrap Equations from the Embedding Space Operator Product Expansion, arXiv:2303.06816

    arXiv

  210. [218]

    Banerjee, K

    S. Banerjee, K. Papadodimas, S. Raju, P. Samantray, and P. Shrivastava,A Bound on Thermal Relativistic Correlators at Large Spacelike Momenta, SciPost Phys.8 (2020), no. 4 064, [arXiv:1902.07203]

    2020 arXiv

  211. [219]

    X J′ 2λn,J′ # τ β 2n! , (A.15) d = 4 GT (τ) = 1 τ 2∆ 1 + 3λ1,2 τ β 4 + ∞X n=2

    S. Caron-Huot and G. D. Moore,Spacelike thermal correlators are almost time independent, Phys. Rev. D106 (2022), no. 12 125015, [arXiv:2209.02641]. 133 A Structure of Scalar Correlator In this appendix we discuss the stress-tensor sector of the thermal two-point function of sc...

    2022 arXiv

  212. [220]

    (K.19) For the relation between thexp basis, (ba,bb,bc) and the (t2,t 4) coefficients that are natural when considering a conformal collider setup, we refer the reader to App

    where one of these can further be traded forCT using the Ward identity CT = 4Sd (d− 2)(d + 3)ba− 2bb− (d + 1)bc d(d + 2) . (K.19) For the relation between thexp basis, (ba,bb,bc) and the (t2,t 4) coefficients that are natural when considering a conformal collider setup, we ref...

    1968

  213. [221]

    189 fixed by Ward identities and the stress-tensor one-point function, while the[T 2]4 and [T 3]6 were computed in [30, 56]

    except through the temperature, the scalar wave equation in Gauss-Bonnet gravity is different from the scalar-channel EoM of metric perturbations. 189 fixed by Ward identities and the stress-tensor one-point function, while the[T 2]4 and [T 3]6 were computed in [30, 56]. Here ...

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.