Pith. sign in

REVIEW 2 major objections 4 minor 70 references

Tantum Gravity

T0 review · 2 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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

Pith's one-line read This paper proposes a corner of quantum gravity — tantum gravity — in which Planck's constant goes to infinity while Newton's constant and the speed of light vanish, and shows that black hole temperature, entropy, and energy remain finite.

desk verdict A new triple-scaling limit with a clean worked example and an honest caveat; the thermodynamic survival claim is conditional on a York-cavity construction that remains open. read the letter →

arxiv 2501.00095 v1 pith:HI24U4CM submitted 2024-12-30 hep-th gr-qcquant-ph

Florian Ecker , Adrien Fiorucci , Daniel Grumiller This is my paper · ORCID
classification hep-thgr-qcquant-ph PACS 04.60.-m04.70.Dy
keywords tantumgravitytriple-scalinglimitCarrollianblackholethermodynamicscoupling-constantcubedilatonHawkingtemperatureCarroll-Schwarzschild
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 paper proposes a new corner of quantum gravity, called tantum gravity, reached by scaling Planck's constant to infinity while Newton's constant and the speed of light go to zero, keeping fixed $G_M=G_N c^{-4}$ and $\kappa=\hbar c$. The authors argue this is the unique limit, up to a dual, in which black hole energy, entropy, temperature, and Schwarzschild radius all stay finite. Demonstrating the construction on spherically symmetric Einstein gravity, the Euclidean action reduces to a finite two-dimensional Carrollian dilaton gravity whose saddle point yields finite black hole thermodynamics and recovers $T=\kappa/(8\pi G_M E)$. If the proposal holds, black hole puzzles become addressable in a limiting theory that retains semi-classical control despite $\hbar\to\infty$.

What carries the argument

The carrying object is the tantum gravity action (12): the $c\to 0$ Carrollian contraction of the spherically reduced Einstein-Hilbert action in two dimensions, augmented by a boundary term that guarantees a finite on-shell action. It depends only on the fixed combinations $G_M$ and $\kappa$, so the $\epsilon\to 0$ limit is finite while the saddle-point approximation is controlled by small $\kappa$. The Carrollian black hole solutions (13), the Carroll-Schwarzschild geometries, are the saddle points, and the constraints in (12) vanish on-shell but are required for Carroll invariance.

What would settle it

Compute the canonical partition function for the tantum black hole saddle inside a finite cavity using the action (12) and its boundary term, then take the cavity radius to infinity; if the on-shell free energy diverges, or if the resulting temperature and entropy are not $T=\kappa/(8\pi G_M E)$ and $S=\pi r_S^2/(\kappa G_M)$, the claim that black hole thermodynamics survives the tantum limit fails.

Watch

Extended reading notes

Core claim

The central claim is that the triple-scaling limit $\hbar\to\infty$, $G_N\to 0$, $c\to 0$ with $G_M=G_N c^{-4}$ and $\kappa=\hbar c$ fixed does not eliminate gravity but defines a finite limiting theory, tantum gravity. Starting from the Euclidean path integral action for spherically symmetric Einstein gravity, the paper performs a Carrollian contraction and obtains the finite two-dimensional dilaton gravity action (12), including a boundary term that keeps the on-shell action finite. Evaluating this action on the Carrollian black hole saddle gives $\ln Z_{\mathrm{TG}}\approx -\beta r_S/(4G_M)$, and the first law then yields $E=r_S/(2G_M)$, $S=\pi r_S^2/(\kappa G_M)$, and $T=\kappa/(4\pi r_S)$, which is exactly the Hawking temperature $T=\kappa/(8\pi G_M E)$. The authors conclude that black hole thermodynamics survives the limit, with black holes defined by their thermal properties rather than by event horizons.

Load-bearing premise

The load-bearing premise is that a well-defined canonical ensemble for the tantum black hole exists, regularized by a cavity construction; the paper's own critical assessment states that this regularization is expected rather than carried out, and the negative specific heat makes the unregularized ensemble formally ill-defined.

Editorial extensions

If this is right

  • Black hole thermodynamics is finite and internally consistent in tantum gravity: the first law holds and the Hawking temperature formula is recovered exactly in the limit.
  • Because the saddle-point approximation is controlled by the small parameter $\kappa$ even though $\hbar$ diverges, tantum gravity provides a semi-classical setting for studying black hole evaporation and related puzzles.
  • The construction extends directly to charged non-rotating black holes and to arbitrary two-dimensional dilaton gravity models, so the same limiting action can serve as a laboratory for lower-dimensional holographic questions.
  • Carrollian black holes in this limit are defined by thermal properties and Carroll extremal surfaces instead of event horizons, which the authors argue aligns with the expectation that genuine quantum black holes are not horizon-defined.
  • The dual antipodal limit, denoted $\mathrm{TG}^*$, is expected to produce a Galilean-type action, and the only smooth route between the two limits passes through full quantum gravity.

Reading between the lines

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

  • If the cavity regularization is carried out explicitly, a concrete check is whether the finite-volume free energy of the tantum black hole approaches the flat-space result smoothly as the cavity wall recedes; a divergence would signal that the thermodynamic saddle is an artifact of the unlimited ensemble.
  • The framework suggests that earlier claims that Carroll partition functions are ill-defined stem from keeping $\hbar$ finite; rescaling $\hbar\sim 1/\epsilon$ as proposed should make the partition function convergent, which a direct evaluation of the Carrollian path integral could test.
  • One could extend the cube-of-limits logic to additional axes such as a cosmological constant or a number of degrees of freedom and ask whether other corners also preserve finite thermodynamics, which would reveal whether tantum gravity is unique or one member of a family.
  • The authors' expectation that rotating black holes are difficult to include points to a concrete obstacle: no finite on-shell tantum action for a Kerr-like Carrollian geometry has been exhibited, and constructing one would be the natural next test.
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

2 major / 4 minor

Summary. The Letter proposes a triple-scaling limit of quantum gravity called 'tantum gravity', in which ℏ → ∞, G_N → 0 and c → 0 while the combinations G_M = G_N c^{-4} and κ = ℏ c are kept fixed. The authors argue from the Hawking temperature formula (1) and the Schwarzschild radius that this is, together with its dual, the only Bronstein-cube corner where black hole temperature, entropy, energy and radius remain finite. They then take this limit in the Euclidean path integral for spherically symmetric Einstein gravity, obtaining the finite two-dimensional Carrollian dilaton-gravity action (12). Evaluating the action on Carroll–Schwarzschild saddles gives a finite free energy (14), and standard thermodynamic manipulations yield finite energy and entropy and recover the Hawking temperature. The paper ends with a critical assessment that identifies the negative-specific-heat problem, the expected York-cavity resolution, and the open rotating case.

Significance. If the ensemble regularization is supplied, this is a valuable contribution: it identifies a previously unappreciated corner of the Bronstein cube in which a saddle-point computation produces finite black hole thermodynamics, with no free parameters and with the boundary term derived rather than fitted. The action-level derivation is independent of the dimensional analysis that motivates the limit, so the finiteness of the on-shell result is nontrivial. The paper is also commendably explicit about its limitations, including the formally ill-defined canonical ensemble and the lack of a generalization to rotating black holes. Its main weakness is that the central thermodynamic claim is conditional on a cavity construction that is promised but not performed.

major comments (2)
  1. [Final critical assessment, after Eq. (14)] The central result (14) is obtained in a canonical ensemble with fixed boundary length ℓ = βκ, but the paper itself acknowledges immediately after (14) that this ensemble is formally ill-defined for the Carroll–Schwarzschild black hole because of negative specific heat, and it only 'expects' York's cavity construction to cure the problem. The cavity boundary terms and the associated stability analysis are not worked out for the Carrollian action (12). Since the free energy, the entropy, and the Hawking-temperature identification all follow from this on-shell saddle-point calculation, the claim that the laws of black hole thermodynamics survive the tantum gravity limit is not established by the computation as it stands.
  2. [Passage after Eq. (13b)] The statement that the flat Carroll solutions can be dropped because 'the latter will have a vanishing on-shell action' is not justified in a canonical ensemble. With the same boundary length ℓ = βκ, a flat r_S = 0 saddle has zero action and hence partition-function weight exp(0) = 1, whereas the Carroll–Schwarzschild saddle has weight exp(−βr_S/4G_M) < 1, so the flat geometry dominates the naive unrestricted ensemble. A reference subtraction or a York cavity is required before Eq. (14) can be interpreted as the black-hole free energy, and neither is provided in the current version.
minor comments (4)
  1. [Footnote 66] Footnote [66] refers to the 'semi-classical limit of the action (13)', but Eq. (13) contains the on-shell solutions, not the action; the intended reference is presumably Eq. (12).
  2. [Eq. (8)] The definition of the boundary volume form and the statement that ℓ = βκ holds 'on dimensional grounds' would benefit from one sentence explaining the normalization of the Euclidean time cycle and the identification β = 1/T, since this boundary condition defines the entire canonical ensemble.
  3. [Main result, Eq. (12)] The expansion leading from the two-dimensional bulk and boundary actions (9)–(10) to the tantum gravity action (12) is delegated to Supplemental Material [26], which is not available in the posted version. Given that Eq. (12) is the main technical result, the revision should include at least a summary of the expansion and of how the Lagrange-multiplier constraints L_v X = 0 and e^μ L_v e_μ = 0 arise.
  4. [Abstract] The abstract states that 'the laws of black hole thermodynamics survive this limit' without qualification, while the derivation treats only the spherically symmetric Schwarzschild sector and explicitly leaves rotating black holes open; a more cautious abstract would reflect this scope.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular reduction: the action derivation and on-shell evaluation are independent, and the final Hawking-formula match is a consistency check rather than a fitted prediction.

full rationale

The paper's derivation chain is not circular in the sense of the seven patterns. The triple-scaling limit (3) is motivated by the desire to keep the Hawking temperature and Schwarzschild radius finite, but the Euclidean action reduction from the spherically symmetric ansatz (5) through the dilaton gravity action (6) to the tantum gravity action (12), including the boundary term (10), is actually performed, not postulated. The free-energy result (14) is a computed saddle-point value from the on-shell action, and no parameter is fitted to a target thermodynamic output. The temperature T = kappa/(4 pi r_S) is cited from the prior Carroll black hole paper [17] by overlapping authors; however, the paper states it can be derived from the absence of conical defects in the Carrollian manifold, and [17] is a published, externally falsifiable result, so the citation constitutes independent support rather than a load-bearing self-citation chain. The final identity T = kappa/(8 pi G_M E) is obtained algebraically from T = kappa/(4 pi r_S) and E = r_S/(2 G_M); since G_M and kappa were defined precisely so that the classical Schwarzschild-radius relation and Hawking formula take this form, the closing 'recovery' of Eq. (1) is an internal-consistency check, not a new prediction. The paper itself flags the remaining gap: 'We glossed over some technical aspects that already arise for Schwarzschild black hole thermodynamics, namely its negative specific heat and its formally ill-defined canonical ensemble... we expect that the same resolution will work as well.' That is an unproven completeness assumption about York's cavity construction, not a circularity. Overall, the central action derivation is self-contained, and the circularity score is low.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

No free parameters are fitted to data; the limit is defined by fixed physical combinations G_M and κ, and the length scale λ drops out of the on-shell thermodynamics. The central claim rests on standard quantum gravity techniques and several domain assumptions, the most fragile being the existence of a well-defined canonical ensemble for the Carroll-Schwarzschild black hole, which the authors defer. No new particles, forces, or dimensions are introduced.

assumptions (5)
  • domain assumption The Euclidean path integral and Gibbons-Hawking saddle-point approximation are valid for quantum gravity.
    Used at the start of the worked example (section 3) to define the partition function as Z≈exp(-Γ/ℏ); this is a standard but unproved assumption in quantum gravity.
  • domain assumption Spherically symmetric Einstein gravity reduces to the 2d dilaton gravity model (6) for the purposes of black hole thermodynamics.
    The paper uses the spherical reduction and explicitly notes in footnote 64 that dimensional reduction and quantization do not commute, but argues the anomaly is irrelevant at leading order.
  • domain assumption A well-defined canonical ensemble exists for the Carroll-Schwarzschild black hole, e.g. via York's cavity construction.
    The authors acknowledge the negative specific heat makes the ensemble formally ill-defined and only expect the cavity resolution to work; the free energy (14) depends on this.
  • domain assumption Black hole temperature in the tantum limit is T=κ/(4π r_S), inherited from Carroll surface gravity.
    The temperature is quoted from [17] and from conical defect regularity, not derived from the partition function in this Letter.
  • domain assumption Saddle-point approximation is valid when κ is small so the action prefactor 1/(κ G_M) is large.
    The paper argues the saddle point is well-defined for small κ, which is a necessary condition for the on-shell evaluation (14).

how reviews work

0 comments
Cite this review

Pith. "Pith review of Tantum Gravity." pith.science (2026). https://pith.science/paper/HI24U4CM

@misc{pith2026250100095,
  author       = {Pith},
  title        = {Pith review of: Tantum Gravity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HI24U4CM}},
  note         = {Machine review of arXiv:2501.00095}
}
abstract

We argue there is an interesting triple-scaling limit of quantum gravity, namely when Planck's constant scales to infinity while Newton's constant and the speed of light tend to zero, keeping fixed the gravitational coupling $G_N\,c^{-4}$ and the combination $\hbar\,c$. We refer to this limiting theory as ``tantum gravity'' and describe in this Letter some of its main properties and prospects for physics. Most notably, the laws of black hole thermodynamics survive this limit, which means that puzzles related to black holes and their evaporation could be addressed more easily in tantum gravity than in fully-fledged quantum gravity.

Figures

Figures reproduced from arXiv: 2501.00095 by the authors.

Figure 1
Figure 1. Bronstein cube with tantum gravity limit high [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

70 extracted references · 24 canonical work pages

  1. [1]

    As long as λ remains finite when ϵ goes to zero, the TG limit ϵ → 0 yields a finite prefactor in front of the action

    work page

  2. [2]

    magnetic limit

    As long as κ is sufficiently small, we can expect a well-defined saddle-point approximation to the Eu- clidean path integral. The Carrollian contraction inherent to the TG limit ϵ → 0 has been performed in [17] along the lines of [13]. To display it, we introduce the inverse partners of the einbein variables defined in the metric (5), τµvµ = 1, eµeµ = 1, ...

    work page

  3. [3]

    Universal Constants, Standard Models and Fundamental Metrology

    G. Cohen-Tannoudji, “Universal Constants, Standard Models and Fundamental Metrology,” Eur. Phys. J. ST 172 (2009) 5–24, 0905.0975

    work page Pith review arXiv 2009

  4. [4]

    Oriti, The Bronstein hypercube of quantum gravity , pp

    D. Oriti, The Bronstein hypercube of quantum gravity , pp. 25–52. Cambridge University Press, 4, 2020. 1803.02577

    arXiv 2020

  5. [5]

    Dimensional reduction in quantum gravity,

    G. ’t Hooft, “Dimensional reduction in quantum gravity,” in Salamfestschrift. World Scientific, 1993. gr-qc/9310026

    arXiv 1993

  6. [6]

    The World as a hologram,

    L. Susskind, “The World as a hologram,” J. Math. Phys. 36 (1995) 6377–6396, hep-th/9409089

    arXiv 1995

  7. [7]

    The large N limit of superconformal field theories and supergravity,

    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

  8. [8]

    Gauge theory correlators from non-critical string theory,

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

    arXiv 1998

Show all 70 references
  1. [9]

    Anti-de Sitter space and holography,

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

    1998 arXiv

  2. [10]

    Holographic derivation of entanglement entropy from AdS/CFT,

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

    2006 arXiv

  3. [11]

    The Information paradox: A Pedagogical introduction,

    S. D. Mathur, “The Information paradox: A Pedagogical introduction,” Class.Quant.Grav. 26 (2009) 224001, 0909.1038

    2009 arXiv

  4. [12]

    Lessons from the information paradox,

    S. Raju, “Lessons from the information paradox,” Phys. Rept. 943 (2022) 1–80, 2012.05770

    2022 arXiv

  5. [13]

    The entropy of Hawking radiation,

    A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian, and A. Tajdini, “The entropy of Hawking radiation,” Rev. Mod. Phys. 93 (2021), no. 3, 035002, 2006.06872

    2021 arXiv

  6. [14]

    The Four laws of black hole mechanics,

    J. M. Bardeen, B. Carter, and S. W. Hawking, “The Four laws of black hole mechanics,” Commun. Math. Phys. 31 (1973) 161–170

    1973

  7. [15]

    Carroll Expansion of General Relativity,

    D. Hansen, N. A. Obers, G. Oling, and B. T. Søgaard, “Carroll Expansion of General Relativity,” SciPost Phys. 13 (2022), no. 3, 055, 2112.12684

    2022 arXiv

  8. [16]

    Magnetic Carrollian gravity from the Carroll algebra,

    A. Campoleoni, M. Henneaux, S. Pekar, A. P´ erez, and P. Salgado-Rebolledo, “Magnetic Carrollian gravity from the Carroll algebra,” JHEP 09 (2022) 127, 2207.14167

    2022 arXiv

  9. [17]

    Une nouvelle limite non-relativiste du groupe de Poincar´ e,

    J.-M. L´ evy-Leblond, “Une nouvelle limite non-relativiste du groupe de Poincar´ e,”Annales de l’I.H.P. Physique th´ eorique3 (1965), no. 1, 1–12

    1965

  10. [18]

    On an analogue of the Galilei group,

    N. D. S. Gupta, “On an analogue of the Galilei group,” Il Nuovo Cimento A (1965-1970) 44 (1966) 512–517

    1966

  11. [19]

    Carroll black holes,

    F. Ecker, D. Grumiller, J. Hartong, A. P´ erez, S. Prohazka, and R. Troncoso, “Carroll black holes,” SciPost Phys. 15 (2023), no. 6, 245, 2308.10947

    2023

  12. [20]

    Black hole explosions,

    S. W. Hawking, “Black hole explosions,” Nature 248 (1974) 30–31

    1974

  13. [21]

    Particle Creation by Black Holes,

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

    1975

  14. [22]

    Action integrals and partition functions in quantum gravity,

    G. W. Gibbons and S. W. Hawking, “Action integrals and partition functions in quantum gravity,” Phys. Rev. D15 (1977) 2752–2756

    1977

  15. [23]

    Hamiltonian formulation of spherically symmetric gravitational fields,

    B. K. Berger, D. M. Chitre, V. E. Moncrief, and Y. Nutku, “Hamiltonian formulation of spherically symmetric gravitational fields,” Phys. Rev. D5 (1972) 2467–2470

    1972

  16. [24]

    Spherically symmetric systems of fields and black holes. 1. 6 Definition and properties of apparent horizon,

    P. Thomi, B. Isaak, and P. H´ aj ´ ıˇ cek, “Spherically symmetric systems of fields and black holes. 1. 6 Definition and properties of apparent horizon,” Phys. Rev. D30 (1984) 1168

    1984

  17. [25]

    Thermodynamics of black holes in two (and higher) dimensions,

    D. Grumiller and R. McNees, “Thermodynamics of black holes in two (and higher) dimensions,” JHEP 04 (2007) 074, hep-th/0703230

    2007 arXiv

  18. [26]

    Lecture notes on holographic renormalization,

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

    2002 arXiv

  19. [27]

    Dilaton gravity in two dimensions,

    D. Grumiller, W. Kummer, and D. V. Vassilevich, “Dilaton gravity in two dimensions,” Phys. Rept. 369 (2002) 327–429, hep-th/0204253

    2002 arXiv

  20. [28]

    See Supplemental Material at [URL will be inserted by publisher] for two ways of holographically renormalizing the action for the spherically-symmetric solution space of tantum gravity

  21. [29]

    Limits of JT gravity,

    D. Grumiller, J. Hartong, S. Prohazka, and J. Salzer, “Limits of JT gravity,” JHEP 02 (2021) 134, 2011.13870

    2021 arXiv

  22. [30]

    Non-relativistic and Carrollian limits of Jackiw-Teitelboim gravity,

    J. Gomis, D. Hidalgo, and P. Salgado-Rebolledo, “Non-relativistic and Carrollian limits of Jackiw-Teitelboim gravity,” JHEP 05 (2021) 162, 2011.15053

    2021 arXiv

  23. [31]

    Asymptotic symmetries in Carrollian theories of gravity,

    A. P´ erez, “Asymptotic symmetries in Carrollian theories of gravity,” JHEP 12 (2021) 173, 2110.15834

    2021 arXiv

  24. [32]

    Carroll stories,

    J. de Boer, J. Hartong, N. A. Obers, W. Sybesma, and S. Vandoren, “Carroll stories,” JHEP 09 (2023) 148, 2307.06827

    2023 arXiv

  25. [33]

    Black hole thermodynamics and the Euclidean Einstein action,

    J. W. York, Jr., “Black hole thermodynamics and the Euclidean Einstein action,” Phys. Rev. D33 (1986) 2092–2099

    1986

  26. [34]

    The Physics of 2-D stringy space-times,

    G. W. Gibbons and M. J. Perry, “The Physics of 2-D stringy space-times,” Int. J. Mod. Phys. D1 (1992) 335–354, hep-th/9204090

    1992 arXiv

  27. [35]

    Thermodynamics of black holes in anti-de Sitter space,

    S. W. Hawking and D. N. Page, “Thermodynamics of black holes in anti-de Sitter space,” Commun. Math. Phys. 87 (1983) 577

    1983

  28. [36]

    On the Dynamics of Near-Extremal Black Holes,

    P. Nayak, A. Shukla, R. M. Soni, S. P. Trivedi, and V. Vishal, “On the Dynamics of Near-Extremal Black Holes,” JHEP 09 (2018) 048, 1802.09547

    2018 arXiv

  29. [37]

    Gravitation and Hamiltonian structure in two space-time dimensions,

    C. Teitelboim, “Gravitation and Hamiltonian structure in two space-time dimensions,” Phys. Lett. B126 (1983) 41

    1983

  30. [38]

    Lower dimensional gravity,

    R. Jackiw, “Lower dimensional gravity,” Nucl. Phys. B252 (1985) 343–356

    1985

  31. [39]

    Some global aspects of string compactifications,

    S. Elitzur, A. Forge, and E. Rabinovici, “Some global aspects of string compactifications,” Nucl. Phys. B359 (1991) 581–610

    1991

  32. [40]

    Classical solutions of two-dimensional string theory,

    G. Mandal, A. M. Sengupta, and S. R. Wadia, “Classical solutions of two-dimensional string theory,” Mod. Phys. Lett. A6 (1991) 1685–1692

    1991

  33. [41]

    On string theory and black holes,

    E. Witten, “On string theory and black holes,” Phys. Rev. D44 (1991) 314–324

    1991

  34. [42]

    A simple model of quantum holography

    A. Kitaev, “A simple model of quantum holography.” KITP strings seminars, April/May 2015, http://online.kitp.ucsb.edu/online/entangled15/ and http://online.kitp.ucsb.edu/online/entangled15/kitaev2/

    2015

  35. [43]

    Gapless spin fluid ground state in a random, quantum Heisenberg magnet,

    S. Sachdev and J. Ye, “Gapless spin fluid ground state in a random, quantum Heisenberg magnet,” Phys. Rev. Lett. 70 (1993) 3339, cond-mat/9212030

    1993 arXiv

  36. [44]

    Holographic metals and the fractionalized Fermi liquid,

    S. Sachdev, “Holographic metals and the fractionalized Fermi liquid,” Phys. Rev. Lett. 105 (2010) 151602, 1006.3794

    2010 arXiv

  37. [45]

    Chaos in AdS 2 Holography,

    K. Jensen, “Chaos in AdS 2 Holography,” Phys. Rev. Lett. 117 (2016), no. 11, 111601, 1605.06098

    2016 arXiv

  38. [46]

    Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space,

    J. Maldacena, D. Stanford, and Z. Yang, “Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space,” PTEP 2016 (2016), no. 12, 12C104, 1606.01857

    2016 arXiv

  39. [47]

    Black Holes and Random Matrices,

    J. S. Cotler, G. Gur-Ari, M. Hanada, J. Polchinski, P. Saad, S. H. Shenker, D. Stanford, A. Streicher, and M. Tezuka, “Black Holes and Random Matrices,” JHEP 05 (2017) 118, 1611.04650. [Erratum: JHEP 09, 002 (2018)]

    2017 arXiv

  40. [48]

    An investigation of AdS2 backreaction and holography,

    J. Engels¨ oy, T. G. Mertens, and H. Verlinde, “An investigation of AdS2 backreaction and holography,” JHEP 07 (2016) 139, 1606.03438

    2016 arXiv

  41. [49]

    The Schwarzian theory — origins,

    T. G. Mertens, “The Schwarzian theory — origins,” JHEP 05 (2018) 036, 1801.09605

    2018 arXiv

  42. [50]

    AdS2 holography and the SYK model,

    G. S´ arosi, “AdS2 holography and the SYK model,” PoS Modave2017 (2018) 001, 1711.08482

    2018 arXiv

  43. [51]

    Notes on the complex Sachdev-Ye-Kitaev model,

    Y. Gu, A. Kitaev, S. Sachdev, and G. Tarnopolsky, “Notes on the complex Sachdev-Ye-Kitaev model,” JHEP 02 (2020) 157, 1910.14099

    2020 arXiv

  44. [52]

    JT gravity as a matrix integral,

    P. Saad, S. H. Shenker, and D. Stanford, “JT gravity as a matrix integral,” 1903.11115

    1903 arXiv

  45. [53]

    Entanglement Wedge Reconstruction and the Information Paradox,

    G. Penington, “Entanglement Wedge Reconstruction and the Information Paradox,” JHEP 09 (2020) 002, 1905.08255

    2020 arXiv

  46. [54]

    The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole,

    A. Almheiri, N. Engelhardt, D. Marolf, and H. Maxfield, “The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole,” JHEP 12 (2019) 063, 1905.08762

    2019 arXiv

  47. [55]

    The Page curve of Hawking radiation from semiclassical geometry,

    A. Almheiri, R. Mahajan, J. Maldacena, and Y. Zhao, “The Page curve of Hawking radiation from semiclassical geometry,” JHEP 03 (2020) 149, 1908.10996

    2020 arXiv

  48. [56]

    Islands outside the horizon,

    A. Almheiri, R. Mahajan, and J. Maldacena, “Islands outside the horizon,” 1910.11077

    1910 arXiv

  49. [57]

    Replica Wormholes and the Entropy of Hawking Radiation,

    A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian, and A. Tajdini, “Replica Wormholes and the Entropy of Hawking Radiation,” JHEP 05 (2020) 013, 1911.12333

    2020 arXiv

  50. [58]

    Replica wormholes and the black hole interior,

    G. Penington, S. H. Shenker, D. Stanford, and Z. Yang, “Replica wormholes and the black hole interior,” JHEP 03 (2022) 205, 1911.11977

    2022 arXiv

  51. [59]

    A universal Schwarzian sector in two-dimensional conformal field theories,

    A. Ghosh, H. Maxfield, and G. J. Turiaci, “A universal Schwarzian sector in two-dimensional conformal field theories,” JHEP 05 (2020) 104, 1912.07654

    2020 arXiv

  52. [60]

    Review on Non-Relativistic Gravity,

    J. Hartong, N. A. Obers, and G. Oling, “Review on Non-Relativistic Gravity,” Front. in Phys. 11 (2023) 1116888, 2212.11309

    2023 arXiv

  53. [61]

    The dimensional-reduction anomaly,

    V. Frolov, P. Sutton, and A. Zelnikov, “The dimensional-reduction anomaly,” Phys. Rev. D61 (2000) 024021, hep-th/9909086

    2000 arXiv

  54. [62]

    Warped Schwarzian theory,

    H. R. Afshar, “Warped Schwarzian theory,” JHEP 02 (2020) 126, 1908.08089

    2020 arXiv

  55. [63]

    Flat space holography and the complex Sachdev-Ye-Kitaev model,

    H. Afshar, H. A. Gonz´ alez, D. Grumiller, and D. Vassilevich, “Flat space holography and the complex Sachdev-Ye-Kitaev model,” Phys. Rev. D 101 (2020), no. 8, 086024, 1911.05739

    2020 arXiv

  56. [64]

    New boundary conditions for AdS2,

    V. Godet and C. Marteau, “New boundary conditions for AdS2,” JHEP 12 (2020) 020, 2005.08999

    2020 arXiv

  57. [65]

    We keep finite the Planck length and energy in both limits but send the Planck time and mass to ∞ in tantum gravity and to 0 in TG ∗

  58. [66]

    dimensional reduction anomaly

    Since, in general, dimensional reduction and quantization do not commute [59] (“dimensional reduction anomaly”) one should think of the spherically 7 reduced theory as a separate quantum gravity model, the classical limit of which coincides with the classical limit of spherica...

  59. [67]

    Inserting the 2d solution (7) back into the 4d metric (5) recovers precisely the Schwarzschild solution

  60. [68]

    However, the latter possibility has to be discarded since it is at odds with our hypotheses to keep the Schwarzschild radius and the energy finite

    The semi-classical limit of the action (13) exists whenever the product κGM is small, which leads to two possible limits, either κ → 0 while keeping GM finite, or GM → 0 while keeping κ finite. However, the latter possibility has to be discarded since it is at odds with our hy...

  61. [69]

    The result for temperature can be derived from the absence of conical defects in the underlying Carrollian manifold; alternatively, the same result follows from a Carrollian version of surface gravity [17]

  62. [70]

    This universal sector has a holographic interpretation in terms of the strongly coupled gravitational dynamics in the throat of near-extremal black holes. For non-extremal black holes there may be a similar story of universal near-horizon dynamics, based on the twisted warped ...

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.