Pith. sign in

REVIEW 4 major objections 5 minor 3 cited by

Butterfly effect and $\textrm{T}\overline{\textrm{T}}$-deformation

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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

Pith's one-line read For T\bar{T}-deformed BTZ black holes, the butterfly velocity is v_B = sqrt(1 - 8π² μ/β²), exceeding the Mezei-Stanford bound for μ<0 while the Lyapunov exponent stays at the maximal value 2π/β.

desk verdict Solid three-method holographic computation of chaos in T\bar{T}-deformed BTZ; clean v_B formula and new rotating extension, but the three-way agreement is internal consistency, not an independent dictionary check. read the letter →

arxiv 2505.14331 v1 pith:XNFEXIEF submitted 2025-05-20 hep-th

Debarshi Basu , Ashish Chandra , Qiang Wen This is my paper · ORCID
classification hep-th
keywords textrmshockwavebutterflychaosdeformedholographicoverlineprobes
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

Holography is a tool that maps a strongly interacting quantum theory to a higher-dimensional gravitational spacetime. In these 'dual' descriptions, chaos in the quantum theory shows up as the growth of tiny perturbations into powerful shockwaves near a black hole horizon. The authors study a specific deformed quantum theory, the T bar-T deformed conformal field theory, which is controlled by a parameter μ. In the holographic picture, this deformation changes the boundary conditions of the black hole spacetime rather than changing the bulk equations.

The authors perturb the deformed black hole and track how a small disturbance scrambles. From shockwave geodesics, pole-skipping locations, and entanglement wedge growth, they extract two chaos parameters: the Lyapunov exponent (how quickly chaos grows in time) and the butterfly velocity (how quickly it spreads in space). All three methods give the same answer: the Lyapunov exponent is maximal, and the butterfly velocity is v_B = sqrt(1 - 8π² μ/β²), where β is the inverse temperature.

For negative μ this velocity is larger than 1, the speed of light in the undeformed theory. This means chaos can spread faster than light in the boundary picture. The paper argues this is not a paradox because the T bar-T deformation makes the theory non-local, changing its effective causal structure. The same behavior is already known for the signal speed in T bar-T theories, so the result connects chaos spreading to this deformed causality. The rotating black hole case is worked out as well, with new formulas for the velocities and a critical value of μ beyond which the theory becomes ill-defined.

Extended reading notes

Core claim

In the T\bar{T}-deformed BTZ black hole, the butterfly velocity is v_B = sqrt(1 - 8π² μ/β²), derived consistently from shockwave OTOCs, pole-skipping, and the entanglement wedge method; for μ<0 this exceeds the Mezei-Stanford bound v_B ≤ 1, while the Lyapunov exponent λ_L = 2π/β saturates the MSS bound (Section 5, eqs. (3.50), (3.71)).

Load-bearing premise

The correspondence between a T\bar{T}-deformed CFT and AdS3 gravity with mixed boundary conditions (eq. (2.7), after [72]) is assumed throughout. If this dictionary fails, the deformed BTZ metric (3.2) and all subsequent shockwave, pole-skipping, and RT computations describe a different theory, and the extracted chaos parameters would not apply to the deformed CFT. The paper also assumes the standard pole-skipping/chaos relation (1.4) and the geodesic approximation (3.29) carry over unchanged to the deformed setting.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The manuscript studies quantum chaos in T\bar{T}-deformed CFT$_2$ through its holographic dual, using the Guica\textendash Monten mixed-boundary-conditions construction of the deformed BTZ black hole. In the non-rotating case the authors construct Kruskal and shockwave geometries, compute OTOCs in the geodesic approximation, and extract the Lyapunov exponent $\lambda_L=2\pi/\beta$ and the butterfly velocity $v_B=\sqrt{1-8\pi^2\mu/\beta^2}$. They reproduce the same $v_B$ from pole-skipping and from the entanglement wedge method, and then extend the pole-skipping and shockwave analysis to rotating deformed BTZ black holes. The paper concludes that for $\mu<0$ the Mezei\textendash Stanford bound $v_B\le 1$ is violated while $\lambda_L$ still saturates the MSS bound.

Significance. If correct, the paper gives an explicit solvable example in which an irrelevant deformation preserves maximal Lyapunov growth but changes the butterfly velocity, including a regime with $v_B>1$. The central formula for $v_B$ is analytic, involves no fitted parameters, and is reproduced by three different holographic probes, which is a useful consistency check. The main caveat is that the three bulk probes all start from the same deformed metric (3.2) built on the dictionary (2.7), so their agreement tests internal consistency of the bulk calculation rather than the T\bar{T}/gravity dictionary itself. The boundary-side argument in Appendix A.2 does provide an independent derivation of $v_B$ from the induced boundary metric, but Appendix A.1, which is the only manifestly field-theoretic perturbative computation, extracts only the Lyapunov exponent and not the spatial profile. The paper is therefore a solid and useful contribution, but its claims of independence and of a field-theoretic derivation of $v_B$ need to be stated more carefully.

major comments (4)
  1. [3.2.1, Eq. (3.45)] Equation (3.45) states $M^2 = 4\pi^2/\beta^2 - 8\pi^2\mu$, which is dimensionally inconsistent (since $\mu$ has dimension length squared, the two terms cannot be subtracted) and is also inconsistent with the quoted result $v_B = \sqrt{1-8\pi^2\mu/\beta^2}$. The correct horizon value obtained from (3.33) is $M^2 = 4L_\mu/(1-2\mu L_\mu)^2 = 4\pi^2/(\beta^2 - 8\pi^2\mu)$. As printed, the shockwave profile (3.48) would not produce the $v_B$ in (3.50). This error must be corrected; the final formula is nevertheless supported by the pole-skipping result (3.62) and the entanglement wedge result (3.71).
  2. [Sections 3 and 5] The paper repeatedly describes the shockwave, pole-skipping, and entanglement wedge computations as independent methods corroborating the result. This overstates the case: all three bulk computations use the same deformed BTZ metric (3.2), obtained from the same dictionary (2.7), and they also share the assumptions that the pole-skipping/chaos relation (1.4) and the geodesic approximation (3.29) survive the deformation unchanged. Their agreement is therefore a consistency check of the bulk calculation, not an independent test of the T\bar{T}/gravity correspondence. The authors should state this limitation explicitly and identify which steps genuinely test the dictionary.
  3. [Appendix A.1] The conformal perturbation theory computation in Appendix A.1 extracts only the Lyapunov exponent from the factor $e^{2\pi t/\beta}$ in (A.14); it does not compute the spatial profile $f_2(x)$, and therefore it does not independently determine the butterfly velocity. The derivation of $v_B$ from field-theoretic considerations rests on the induced boundary metric argument in Appendix A.2, not on the perturbative OTOC computation. This gap should be acknowledged so that the reader understands which parts of the chaos data are derived from the deformed field theory and which are assumed from the holographic dictionary.
  4. [Sections 1 and 3.3] The paper assumes without comment that the pole-skipping/chaos dictionary (1.4) and the geodesic approximation (3.29) carry over unchanged to the deformed setting. Because the T\bar{T} deformation is an irrelevant, non-local deformation, an $O(\mu)$ correction to either relation would shift all three bulk results together and would change the extracted $v_B$ even if the metric (3.2) is correct. The authors should at least state this assumption explicitly and, if possible, provide a check of (1.4) at first order in $\mu$ from a direct boundary computation of the energy-density correlator.
minor comments (5)
  1. [Equations (3.20) and (3.43)] The symbol $M$ is used both for the black hole mass in Section 3.1 and for the mass parameter $M(u,v)$ in the localized shockwave equation (3.43). This overloaded notation makes the shockwave derivation harder to follow; one of the two should be renamed.
  2. [Equation (3.28)] The expression involving $\epsilon_c$ and the factor $(\beta - \sqrt{\beta^2-8\pi^2\mu})/(4\pi\mu)$ appears singular as $\mu\to 0$; it would help to state explicitly how this limit is taken and to define $\epsilon_c$ before use.
  3. [Section 4.1, Eq. (4.14)] The quantities $\beta_+$ and $\beta_-$ are used in (4.14) and (4.15) but are not defined before this point; the authors should define them, for example in terms of $r_\pm$ or of $\beta$ and $\Omega$.
  4. [Appendix A.1, text after Eq. (A.8)] The phrase “conformal blacks” should read “conformal blocks”, and the sentence beginning “The four-point function on the complex plane may be expanded in terms of conformal blacks” should be rephrased for clarity.
  5. [Section 5] The statement that the field-theoretic analysis in Appendix A provides “consistent results of the OTOC up to linear order in $\mu$” is slightly misleading: as noted above, it determines $\lambda_L$ but not $v_B$. The wording should be adjusted to match what is actually computed.
Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The central result v_B = sqrt(1 - 8π² μ/β²) is derived without fitting. The only inputs are the deformation parameter μ and temperature β, both physical parameters of the T\bar{T}-deformed CFT. The shockwave, pole-skipping, and RT computations are independent probes of the same bulk geometry; no new fields or tunable constants are introduced.

assumptions (5)
  • domain assumption The T\bar{T}-deformed CFT is holographically dual to AdS3 gravity with mixed boundary conditions (Guica-Monten dictionary, eq. (2.7)).
    Section 2 'Holography'. Used to construct the deformed BTZ metric (3.2). If this dictionary is invalid, the bulk computations do not describe the deformed CFT.
  • domain assumption The geodesic approximation relates the OTOC to e^{-m d} in the shockwave geometry (eq. (3.29)).
    Section 3.1.1. Assumes large probe mass and saddle point dominance of the gravitational path integral.
  • domain assumption The pole-skipping/chaos relation (ω_*, k_*) = (i λ_L, i λ_L/v_B) holds for deformed holographic theories (eq. (1.4)).
    Section 3.3. Imported from [34]; used to extract chaos parameters from pole-skipping points.
  • domain assumption The shockwave ansatz v → v + α(x)Θ(u) with only the uu metric component modified is valid at leading order (eqs. (3.38)-(3.40)).
    Section 3.2.1. Inherited from Dray-'t Hooft / Sfetsos; assumes linearized backreaction suffices.
  • domain assumption For the rotating case, the angular coordinate is taken non-compact (high temperature limit) before imposing periodicity to extract chaos parameters.
    Sections 4.1 and 4.2.1. Pole-skipping and shockwave computations are performed in the high-temperature limit; periodicity is imposed afterward following [101,103].

how reviews work

0 comments
Cite this review

Pith. "Pith review of Butterfly effect and $\textrm{T}\overline{\textrm{T}}$-deformation." pith.science (2026). https://pith.science/paper/XNFEXIEF

@misc{pith2026250514331,
  author       = {Pith},
  title        = {Pith review of: Butterfly effect and $\textrmT\overline\textrmT$-deformation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XNFEXIEF}},
  note         = {Machine review of arXiv:2505.14331}
}
abstract

These notes present a comprehensive analysis of shockwave geometries in holographic settings, focusing on $\textrm{T}\overline{\textrm{T}}$-deformed BTZ black holes and their extensions. By constructing deformed metrics and employing Kruskal coordinates, we examine out-of-time-ordered correlators (OTOCs) as probes of quantum chaos. We also study localized shockwave solutions and analyze their backreaction, highlighting regimes in which the Mezei-Stanford bound on the butterfly velocity is potentially violated. The results obtained via shockwave methods are corroborated with recent developments in pole-skipping phenomena and the entanglement wedge approach, demonstrating consistency among distinct probes of chaos in holographic theories.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. High-Order Pole-Skipping in Near-Extremal Holography

    hep-th 2026-07 conditional novelty 7.0 of 10

    In near-extremal holographic black holes, the n-th order pole-skipping momentum with mode index q becomes order-independent as T→0: k²_{n,q} → −m²h(r_h) + ½q(q−1)h(r_h)f″(r_h), with q identified as the AdS2 IR conform...

  2. Charged Black Hole with String Cloud Deformation: Entanglement and Chaos

    hep-th 2025-07 conditional novelty 4.0 of 10

    In a charged AdS black hole with a string cloud, entanglement entropy and entanglement wedge cross-section increase with charge and backreaction, while mutual information and butterfly velocity decrease with charge.

  3. Comparative study of the butterfly velocity in holographic QCD models at finite temperature and chemical potential

    hep-th 2025-05 conditional novelty 4.0 of 10

    Using three independent holographic methods, the authors obtain matching butterfly velocities for four QCD-like models and find a universal increase with temperature and decrease with chemical potential.

Reference graph

Works this paper leans on

112 extracted references · 8 canonical work pages · cited by 3 Pith papers

  1. [1]

    F. A. Dolan and H. Osborn,Conformal four point functions and the operator product expansion, Nucl. Phys. B 599 (2001) 459 [hep-th/0011040]

    arXiv 2001

  2. [2]

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

    arXiv 2014

  3. [3]

    D. A. Roberts and D. Stanford,Two-dimensional conformal field theory and the butterfly effect, Phys. Rev. Lett.115 (2015) 131603 [1412.5123]. – 33 –

    arXiv 2015

  4. [4]

    Grozdanov, K

    S. Grozdanov, K. Schalm and V. Scopelliti,Black hole scrambling from hydrodynamics, Phys. Rev. Lett.120 (2018) 231601 [1710.00921]

    arXiv 2018

  5. [5]

    Mezei and D

    M. Mezei and D. Stanford,On entanglement spreading in chaotic systems, JHEP 05 (2017) 065 [1608.05101]

    arXiv 2017

  6. [6]

    Sekino and L

    Y. Sekino and L. Susskind,Fast Scramblers, JHEP 10 (2008) 065 [0808.2096]

    arXiv 2008

  7. [7]

    S. H. Shenker and D. Stanford,Black holes and the butterfly effect, JHEP 03 (2014) 067 [1306.0622]

    arXiv 2014

  8. [8]

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

    arXiv 1998

Show all 112 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 [hep-th/9802109]

    1998 arXiv

  2. [10]

    Xu and B

    S. Xu and B. Swingle,Locality, Quantum Fluctuations, and Scrambling, Phys. Rev. X 9 (2019) 031048 [1805.05376]

    2019 arXiv

  3. [11]

    Gharibyan, M

    H. Gharibyan, M. Hanada, B. Swingle and M. Tezuka,Quantum Lyapunov Spectrum, JHEP 04 (2019) 082 [1809.01671]

    2019 arXiv

  4. [12]

    Steinberg and B

    J. Steinberg and B. Swingle,Thermalization and chaos in QED3, Phys. Rev. D99 (2019) 076007 [1901.04984]

    2019 arXiv

  5. [13]

    Y. Gu, A. Kitaev and P. Zhang,A two-way approach to out-of-time-order correlators, JHEP 03 (2022) 133 [2111.12007]

    2022 arXiv

  6. [14]

    R. R. Poojary,BTZ dynamics and chaos, JHEP 03 (2020) 048 [1812.10073]

    2020 arXiv

  7. [15]

    Banerjee, A

    A. Banerjee, A. Kundu and R. R. Poojary,Strings, branes, Schwarzian action and maximal chaos, Phys. Lett. B838 (2023) 137632 [1809.02090]

    2023 arXiv

  8. [16]

    Malvimat and R

    V. Malvimat and R. R. Poojary,Fast scrambling due to rotating shockwaves in BTZ, Phys. Rev. D 105 (2022) 126019 [2112.14089]

    2022 arXiv

  9. [17]

    S. Das, B. Ezhuthachan, A. Kundu, S. Porey, B. Roy and K. Sengupta,Out-of-Time-Order correlators in driven conformal field theories, JHEP 08 (2022) 221 [2202.12815]

    2022 arXiv

  10. [18]

    S. Das, B. Ezhuthachan, A. Kundu, S. Porey and B. Roy,Critical quenches, OTOCs and early-time chaos, JHEP 07 (2022) 046 [2108.12884]

    2022 arXiv

  11. [19]

    S. Das, B. Ezhuthachan and A. Kundu,Real time dynamics from low point correlators in 2d BCFT, JHEP 12 (2019) 141 [1907.08763]

    2019 arXiv

  12. [20]

    R. Fan, P. Zhang, H. Shen and H. Zhai,Out-of-Time-Order Correlation for Many-Body Localization, Sci. Bull. 62 (2017) 707 [1608.01914]

    2017 arXiv

  13. [21]

    Biswas, B

    P. Biswas, B. Ezhuthachan, A. Kundu and B. Roy,Moving mirrors, OTOCs and scrambling, JHEP 10 (2024) 146 [2406.05772]

    2024 arXiv

  14. [22]

    Baishya, A

    B. Baishya, A. Chakraborty and N. Padhi,A study of three butterflies: entanglement wedge method, OTOC and pole-skipping, 2406.18319

    arXiv

  15. [23]

    Banerjee, A

    A. Banerjee, A. Bhattacharyya, P. Drashni and S. Pawar,From CFTs to theories with Bondi-Metzner-Sachs symmetries: Complexity and out-of-time-ordered correlators, Phys. Rev. D 106 (2022) 126022 [2205.15338]

    2022 arXiv

  16. [24]

    Xu and B

    S. Xu and B. Swingle,Scrambling Dynamics and Out-of-Time-Ordered Correlators in Quantum Many-Body Systems, PRX Quantum 5 (2024) 010201 [2202.07060]. – 34 –

    2024 arXiv

  17. [25]

    S. Das, B. Ezhuthachan, A. Kundu, S. Porey, B. Roy and K. Sengupta,Brane detectors of a dynamical phase transition in a driven CFT, SciPost Phys. 15 (2023) 202 [2212.04201]

    2023 arXiv

  18. [26]

    Hashimoto, K.-B

    K. Hashimoto, K.-B. Huh, K.-Y. Kim and R. Watanabe,Exponential growth of out-of-time-order correlator without chaos: inverted harmonic oscillator, JHEP 11 (2020) 068 [2007.04746]

    2020 arXiv

  19. [27]

    Khetrapal,Chaos and operator growth in 2d CFT, JHEP 03 (2023) 176 [2210.15860]

    S. Khetrapal,Chaos and operator growth in 2d CFT, JHEP 03 (2023) 176 [2210.15860]

    2023 arXiv

  20. [28]

    Perlmutter,Bounding the Space of Holographic CFTs with Chaos, JHEP 10 (2016) 069 [1602.08272]

    E. Perlmutter,Bounding the Space of Holographic CFTs with Chaos, JHEP 10 (2016) 069 [1602.08272]

    2016 arXiv

  21. [29]

    D. A. Roberts, D. Stanford and L. Susskind,Localized shocks, JHEP 03 (2015) 051 [1409.8180]

    2015 arXiv

  22. [30]

    Ryu and T

    S. Ryu and T. Takayanagi,Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett.96 (2006) 181602 [hep-th/0603001]

    2006 arXiv

  23. [31]

    Ryu and T

    S. Ryu and T. Takayanagi,Aspects of Holographic Entanglement Entropy, JHEP 08 (2006) 045 [hep-th/0605073]

    2006 arXiv

  24. [32]

    V. E. Hubeny, M. Rangamani and T. Takayanagi,A Covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [0705.0016]

    2007 arXiv

  25. [33]

    Maldacena, S

    J. Maldacena, S. H. Shenker and D. Stanford,A bound on chaos, JHEP 08 (2016) 106 [1503.01409]

    2016 arXiv

  26. [34]

    Blake, R

    M. Blake, R. A. Davison, S. Grozdanov and H. Liu,Many-body chaos and energy dynamics in holography, JHEP 10 (2018) 035 [1809.01169]

    2018 arXiv

  27. [35]

    Blake, H

    M. Blake, H. Lee and H. Liu,A quantum hydrodynamical description for scrambling and many-body chaos, JHEP 10 (2018) 127 [1801.00010]

    2018 arXiv

  28. [36]

    Grozdanov,On the connection between hydrodynamics and quantum chaos in holographic theories with stringy corrections, JHEP 01 (2019) 048 [1811.09641]

    S. Grozdanov,On the connection between hydrodynamics and quantum chaos in holographic theories with stringy corrections, JHEP 01 (2019) 048 [1811.09641]

    2019 arXiv

  29. [37]

    Blake, R

    M. Blake, R. A. Davison and D. Vegh,Horizon constraints on holographic Green’s functions, JHEP 01 (2020) 077 [1904.12883]

    2020 arXiv

  30. [38]

    Cardy,The T T deformation of quantum field theory as random geometry, JHEP 10 (2018) 186 [1801.06895]

    J. Cardy,The T T deformation of quantum field theory as random geometry, JHEP 10 (2018) 186 [1801.06895]

    2018 arXiv

  31. [39]

    Dubovsky, V

    S. Dubovsky, V. Gorbenko and G. Hernández-Chifflet,T T partition function from topological gravity, JHEP 09 (2018) 158 [1805.07386]

    2018 arXiv

  32. [40]

    Datta and Y

    S. Datta and Y. Jiang,T ¯T deformed partition functions, JHEP 08 (2018) 106 [1806.07426]

    2018 arXiv

  33. [41]

    Aharony, S

    O. Aharony, S. Datta, A. Giveon, Y. Jiang and D. Kutasov,Modular invariance and uniqueness of T ¯T deformed CFT, JHEP 01 (2019) 086 [1808.02492]

    2019 arXiv

  34. [42]

    A. B. Zamolodchikov,Expectation value of composite field T anti-T in two-dimensional quantum field theory, hep-th/0401146

    arXiv

  35. [43]

    Cavaglià, S

    A. Cavaglià, S. Negro, I. M. Szécsényi and R. Tateo,T ¯T-deformed 2D Quantum Field Theories, JHEP 10 (2016) 112 [1608.05534]

    2016 arXiv

  36. [44]

    F. A. Smirnov and A. B. Zamolodchikov,On space of integrable quantum field theories, Nucl. Phys. B 915 (2017) 363 [1608.05499]

    2017 arXiv

  37. [45]

    He and H

    S. He and H. Shu,Correlation functions, entanglement and chaos in theT T /JT-deformed CFTs, JHEP 02 (2020) 088 [1907.12603]. – 35 –

    2020 arXiv

  38. [46]

    S. He, Y. Sun and Y.-X. Zhang,T T-flow effects on torus partition functions, JHEP 09 (2021) 061 [2011.02902]

    2021 arXiv

  39. [47]

    S. He, P. H. C. Lau, Z.-Y. Xian and L. Zhao,Quantum chaos, scrambling and operator growth in T T deformed SYK models, JHEP 12 (2022) 070 [2209.14936]

    2022 arXiv

  40. [48]

    S. He, J. Yang, Y.-X. Zhang and Z.-X. Zhao,Pseudo entropy of primary operators in T T /JT-deformed CFTs, JHEP 09 (2023) 025 [2305.10984]

    2023 arXiv

  41. [49]

    Tian,On-shell action of T¯T-deformed Holographic CFTs, 2306.01258

    J. Tian,On-shell action of T¯T-deformed Holographic CFTs, 2306.01258

    arXiv

  42. [50]

    J. Tian, T. Lai and F. Omidi,Modular transformations of on-shell actions of (root-)T¯T deformed holographic CFTs, Nucl. Phys. B 1007 (2024) 116675 [2404.16354]

    2024 arXiv

  43. [51]

    M. He, J. Hou and Y. Jiang,T T-deformed entanglement entropy for IQFT, JHEP 03 (2024) 056 [2306.07784]

    2024 arXiv

  44. [52]

    He and Y

    M. He and Y. Sun,Holographic entanglement entropy inT T-deformed AdS3, Nucl. Phys. B 990 (2023) 116190 [2301.04435]

    2023 arXiv

  45. [53]

    He,One-loop partition functions inT T-deformed AdS3, JHEP 05 (2024) 067 [2401.09879]

    M. He,One-loop partition functions inT T-deformed AdS3, JHEP 05 (2024) 067 [2401.09879]

    2024 arXiv

  46. [54]

    Dubovsky, V

    S. Dubovsky, V. Gorbenko and M. Mirbabayi,Asymptotic fragility, near AdS2 holography and T T, JHEP 09 (2017) 136 [1706.06604]

    2017 arXiv

  47. [55]

    Callebaut, J

    N. Callebaut, J. Kruthoff and H. Verlinde,T T deformed CFT as a non-critical string, JHEP 04 (2020) 084 [1910.13578]

    2020 arXiv

  48. [56]

    A. J. Tolley,T T deformations, massive gravity and non-critical strings, JHEP 06 (2020) 050 [1911.06142]

    2020 arXiv

  49. [57]

    McGough, M

    L. McGough, M. Mezei and H. Verlinde,Moving the CFT into the bulk withT T, JHEP 04 (2018) 010 [1611.03470]

    2018 arXiv

  50. [58]

    Kraus, J

    P. Kraus, J. Liu and D. Marolf,Cutoff AdS3 versus the T T deformation, JHEP 07 (2018) 027 [1801.02714]

    2018 arXiv

  51. [59]

    Taylor, T ¯T deformations in general dimensions, Adv

    M. Taylor, T ¯T deformations in general dimensions, Adv. Theor. Math. Phys.27 (2023) 37 [1805.10287]

    2023 arXiv

  52. [60]

    Kraus, R

    P. Kraus, R. Monten and K. Roumpedakis,Refining the cutoff 3d gravity/T T correspondence, JHEP 10 (2022) 094 [2206.00674]

    2022 arXiv

  53. [61]

    Asrat, A

    M. Asrat, A. Giveon, N. Itzhaki and D. Kutasov,Holography Beyond AdS, Nucl. Phys. B 932 (2018) 241 [1711.02690]

    2018 arXiv

  54. [62]

    Shyam,Background independent holographic dual toT ¯T deformed CFT with large central charge in 2 dimensions, JHEP 10 (2017) 108 [1707.08118]

    V. Shyam,Background independent holographic dual toT ¯T deformed CFT with large central charge in 2 dimensions, JHEP 10 (2017) 108 [1707.08118]

    2017 arXiv

  55. [63]

    Cottrell and A

    W. Cottrell and A. Hashimoto,Comments on T ¯T double trace deformations and boundary conditions, Phys. Lett. B789 (2019) 251 [1801.09708]

    2019 arXiv

  56. [64]

    Hartman, J

    T. Hartman, J. Kruthoff, E. Shaghoulian and A. Tajdini,Holography at finite cutoff with a T 2 deformation, JHEP 03 (2019) 004 [1807.11401]

    2019 arXiv

  57. [65]

    Shyam,Finite Cutoff AdS5 Holography and the Generalized Gradient Flow, JHEP 12 (2018) 086 [1808.07760]

    V. Shyam,Finite Cutoff AdS5 Holography and the Generalized Gradient Flow, JHEP 12 (2018) 086 [1808.07760]

    2018 arXiv

  58. [66]

    Caputa, S

    P. Caputa, S. Datta and V. Shyam,Sphere partition functions \& cut-off AdS, JHEP 05 (2019) 112 [1902.10893]. – 36 –

    2019 arXiv

  59. [67]

    Lewkowycz, J

    A. Lewkowycz, J. Liu, E. Silverstein and G. Torroba,T T and EE, with implications for (A)dS subregion encodings, JHEP 04 (2020) 152 [1909.13808]

    2020

  60. [68]

    Giveon, N

    A. Giveon, N. Itzhaki and D. Kutasov,A solvable irrelevant deformation of AdS3/CFT2, JHEP 12 (2017) 155 [1707.05800]

    2017 arXiv

  61. [69]

    Chang, S

    J.-C. Chang, S. He, Y.-X. Liu and L. Zhao,The holographic T ¯T deformation of the entanglement entropy in (A)dS3/CFT2, 2409.08198

    arXiv

  62. [70]

    Apolo, P.-X

    L. Apolo, P.-X. Hao, W.-X. Lai and W. Song,Glue-on AdS holography forT T-deformed CFTs, JHEP 06 (2023) 117 [2303.04836]

    2023 arXiv

  63. [71]

    Apolo, P.-X

    L. Apolo, P.-X. Hao, W.-X. Lai and W. Song,Extremal surfaces in glue-on AdS/T T holography, JHEP 01 (2024) 054 [2311.04883]

    2024 arXiv

  64. [72]

    Guica and R

    M. Guica and R. Monten,T ¯T and the mirage of a bulk cutoff, SciPost Phys. 10 (2021) 024 [1906.11251]

    2021 arXiv

  65. [73]

    Hirano and M

    S. Hirano and M. Shigemori,Random boundary geometry and gravity dual ofT T deformation, JHEP 11 (2020) 108 [2003.06300]

    2020 arXiv

  66. [74]

    Hirano, T

    S. Hirano, T. Nakajima and M. Shigemori,T T Deformation of stress-tensor correlators from random geometry, JHEP 04 (2021) 270 [2012.03972]

    2021 arXiv

  67. [75]

    Faulkner, H

    T. Faulkner, H. Liu and M. Rangamani,Integrating out geometry: Holographic Wilsonian RG and the membrane paradigm, JHEP 08 (2011) 051 [1010.4036]

    2011 arXiv

  68. [76]

    Heemskerk and J

    I. Heemskerk and J. Polchinski,Holographic and Wilsonian Renormalization Groups, JHEP 06 (2011) 031 [1010.1264]

    2011 arXiv

  69. [77]

    Balasubramanian, M

    V. Balasubramanian, M. Guica and A. Lawrence,Holographic Interpretations of the Renormalization Group, JHEP 01 (2013) 115 [1211.1729]

    2013 arXiv

  70. [78]

    Jiang,A pedagogical review on solvable irrelevant deformations of 2D quantum field theory, Commun

    Y. Jiang,A pedagogical review on solvable irrelevant deformations of 2D quantum field theory, Commun. Theor. Phys.73 (2021) 057201 [1904.13376]

    2021 arXiv

  71. [79]

    S. He, Y. Li, H. Ouyang and Y. Sun,T T Deformation: Introduction and Some Recent Advances, 2503.09997

    arXiv

  72. [80]

    Skenderis and S

    K. Skenderis and S. N. Solodukhin,Quantum effective action from the AdS / CFT correspondence, Phys. Lett. B472 (2000) 316 [hep-th/9910023]

    2000 arXiv

  73. [81]

    Banados,Three-dimensional quantum geometry and black holes, AIP Conf

    M. Banados,Three-dimensional quantum geometry and black holes, AIP Conf. Proc.484 (1999) 147 [hep-th/9901148]

    1999 arXiv

  74. [82]

    Banerjee and P

    A. Banerjee and P. Roy,Bounds on T ¯T deformation from entanglement, 2404.16946

    arXiv

  75. [83]

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

    2003 arXiv

  76. [84]

    Hartman and J

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

    2013 arXiv

  77. [85]

    Dray and G

    T. Dray and G. ’t Hooft,The Gravitational Shock Wave of a Massless Particle, Nucl. Phys. B 253 (1985) 173

    1985

  78. [86]

    Dray and G

    T. Dray and G. ’t Hooft,The Effect of Spherical Shells of Matter on the Schwarzschild Black Hole, Commun. Math. Phys.99 (1985) 613

    1985

  79. [87]

    Hotta and M

    M. Hotta and M. Tanaka,Shock wave geometry with nonvanishing cosmological constant, Class. Quant. Grav.10 (1993) 307. – 37 –

    1993

  80. [88]

    Sfetsos,On gravitational shock waves in curved space-times, Nucl

    K. Sfetsos,On gravitational shock waves in curved space-times, Nucl. Phys. B 436 (1995) 721 [hep-th/9408169]

    1995 arXiv

  81. [89]

    Cai and J

    R.-G. Cai and J. B. Griffiths,Null particle solutions in three-dimensional (anti-)de Sitter spaces, J. Math. Phys.40 (1999) 3465 [gr-qc/9905011]

    1999 arXiv

  82. [90]

    Cornalba, M

    L. Cornalba, M. S. Costa, J. Penedones and R. Schiappa,Eikonal Approximation in AdS/CFT: From Shock Waves to Four-Point Functions, JHEP 08 (2007) 019 [hep-th/0611122]

    2007 arXiv

  83. [91]

    S. H. Shenker and D. Stanford,Stringy effects in scrambling, JHEP 05 (2015) 132 [1412.6087]

    2015 arXiv

  84. [92]

    Qi and Z

    X.-L. Qi and Z. Yang,Butterfly velocity and bulk causal structure, 1705.01728

    arXiv

  85. [93]

    Fischler, V

    W. Fischler, V. Jahnke and J. F. Pedraza,Chaos and entanglement spreading in a non-commutative gauge theory, JHEP 11 (2018) 072 [1808.10050]

    2018 arXiv

  86. [94]

    Dubovsky, R

    S. Dubovsky, R. Flauger and V. Gorbenko,Solving the Simplest Theory of Quantum Gravity, JHEP 09 (2012) 133 [1205.6805]

    2012 arXiv

  87. [95]

    Liu and A

    Y. Liu and A. Raju,Quantum Chaos in Topologically Massive Gravity, JHEP 12 (2020) 027 [2005.08508]

    2020 arXiv

  88. [96]

    Ceplak and D

    N. Ceplak and D. Vegh,Pole-skipping and Rarita-Schwinger fields, Phys. Rev. D103 (2021) 106009 [2101.01490]

    2021 arXiv

  89. [97]

    X. Dong, D. Wang, W. W. Weng and C.-H. Wu,A tale of two butterflies: an exact equivalence in higher-derivative gravity, JHEP 10 (2022) 009 [2203.06189]

    2022 arXiv

  90. [98]

    Malvimat and R

    V. Malvimat and R. R. Poojary,Fast scrambling of mutual information in Kerr-AdS5, JHEP 03 (2023) 099 [2210.02950]

    2023 arXiv

  91. [99]

    Malvimat and R

    V. Malvimat and R. R. Poojary,Fast scrambling of mutual information in Kerr-AdS4 spacetime, Phys. Rev. D107 (2023) 026019 [2207.13022]

    2023 arXiv

  92. [100]

    Craps, S

    B. Craps, S. Khetrapal and C. Rabideau,Chaos in CFT dual to rotating BTZ, JHEP 11 (2021) 105 [2107.13874]

    2021 arXiv

  93. [101]

    Jahnke, K.-Y

    V. Jahnke, K.-Y. Kim and J. Yoon,On the Chaos Bound in Rotating Black Holes, JHEP 05 (2019) 037 [1903.09086]

    2019 arXiv

  94. [102]

    Basu and S

    D. Basu and S. Biswas,Entanglement, TT and rotating black holes, JHEP 03 (2025) 167 [2410.06363]

    2025 arXiv

  95. [103]

    Mezei and G

    M. Mezei and G. Sárosi,Chaos in the butterfly cone, JHEP 01 (2020) 186 [1908.03574]

    2020 arXiv

  96. [104]

    D. E. Parker, X. Cao, A. Avdoshkin, T. Scaffidi and E. Altman,A Universal Operator Growth Hypothesis, Phys. Rev. X 9 (2019) 041017 [1812.08657]

    2019 arXiv

  97. [105]

    Dymarsky and M

    A. Dymarsky and M. Smolkin,Krylov complexity in conformal field theory, Phys. Rev. D 104 (2021) L081702 [2104.09514]

    2021 arXiv

  98. [106]

    Kundu, V

    A. Kundu, V. Malvimat and R. Sinha,State dependence of Krylov complexity in 2d CFTs, JHEP 09 (2023) 011 [2303.03426]

    2023 arXiv

  99. [107]

    Fan,Momentum-Krylov complexity correspondence, 2411.04492

    Z.-Y. Fan,Momentum-Krylov complexity correspondence, 2411.04492

    arXiv

  100. [108]

    Chattopadhyay, V

    A. Chattopadhyay, V. Malvimat and A. Mitra,Krylov complexity of deformed conformal field theories, JHEP 08 (2024) 053 [2405.03630]. – 38 –

    2024 arXiv

  101. [109]

    Jeong, K.-Y

    H.-S. Jeong, K.-Y. Kim and M. Nishida,Entanglement and Rényi entropy of multiple intervals in T T-deformed CFT and holography, Phys. Rev. D100 (2019) 106015 [1906.03894]

    2019 arXiv

  102. [110]

    Basu, Lavish and B

    D. Basu, Lavish and B. Paul,Entanglement negativity in TT¯-deformed CFT2s, Phys. Rev. D 107 (2023) 126026 [2302.11435]

    2023

  103. [111]

    Basu and V

    D. Basu and V. Raj,Reflected entropy and timelike entanglement in TT¯-deformed CFT2s, Phys. Rev. D110 (2024) 046009 [2402.07253]

    2024 arXiv

  104. [112]

    B. Chen, L. Chen and P.-X. Hao,Entanglement entropy inT T-deformed CFT, Phys. Rev. D 98 (2018) 086025 [1807.08293]. – 39 –

    2018 arXiv

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.