pith. sign in

arxiv: 2508.03236 · v3 · pith:Z5XIID4Jnew · submitted 2025-08-05 · ✦ hep-th

Timelike Liouville theory and AdS₃ gravity at finite cutoff

Kuroush Allameh , Edgar Shaghoulian This is my paper

Pith reviewed 2026-05-22 00:13 UTC · model grok-4.3

classification ✦ hep-th
keywords AdS3 gravityfinite cutofftimelike Liouville theoryconformal boundary conditionsholographic CFT2marginal deformationflat space dualitypartition functions
0
0 comments X

The pith

AdS3 gravity at finite cutoff is dual to a CFT2 coupled to timelike Liouville theory via a marginal deformation, with the Liouville field setting the radial wall position.

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

The paper proposes that three-dimensional anti-de Sitter gravity with conformal boundary conditions and a finite radial cutoff is captured by a two-dimensional boundary theory consisting of the usual holographic CFT coupled to timelike Liouville theory. An exactly marginal deformation is added to this combined theory. The Liouville field is interpreted as the dynamical variable that determines the location of the cutoff surface in the bulk. The authors verify the proposal in the semiclassical regime by showing that the sphere and torus partition functions agree with the bulk gravitational path integral. They further demonstrate that the classical equation of motion for the Liouville field reproduces the Hamiltonian constraint of the bulk theory.

Core claim

AdS3 gravity with conformal boundary conditions is described by coupling the holographic CFT2 to timelike Liouville theory and deforming by an exactly marginal operator; the Liouville field controls the finite-cutoff radial wall in the bulk. This is checked semiclassically by matching sphere and torus partition functions and by verifying that the Liouville equation of motion yields the bulk Hamiltonian constraint. The strong-coupling limit of the boundary theory corresponds to pushing the cutoff deep inside black-hole interiors and simultaneously yields a duality between three-dimensional flat space and a two-dimensional CFT.

What carries the argument

Timelike Liouville theory coupled to the holographic CFT2 with an exactly marginal deformation; the Liouville field functions as the dynamical coordinate that locates the finite radial cutoff surface.

If this is right

  • Sphere and torus partition functions of the bulk theory are reproduced by the deformed Liouville-CFT system in the semiclassical limit.
  • The classical Liouville equation of motion is identical to the Hamiltonian constraint of the bulk gravity theory.
  • Taking the strong-coupling limit of the boundary theory moves the cutoff surface inside black-hole geometries and recovers a flat-space duality.
  • The radial cutoff position is now a dynamical field rather than a fixed parameter.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The construction may allow systematic computation of finite-cutoff observables using known Liouville correlation functions.
  • Similar couplings could be explored for higher-dimensional AdS gravity with finite cutoffs.
  • The flat-space limit suggests a concrete route to test flat-space holography through Liouville techniques.
  • One could look for a direct dictionary between Liouville operators and bulk operators inserted behind the cutoff.

Load-bearing premise

Semiclassical matching of partition functions together with the Liouville equation reproducing the bulk Hamiltonian constraint is enough to establish the duality for the full quantum theory.

What would settle it

A mismatch between the bulk and boundary partition functions on a higher-genus surface or at strong quantum corrections would disprove the proposed equivalence.

Figures

Figures reproduced from arXiv: 2508.03236 by Edgar Shaghoulian, Kuroush Allameh.

Figure 1
Figure 1. Figure 1: (a) The Penrose diagram for the non-rotating BTZ geometry. Only black-hole [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a) The Penrose diagram for Rindler space, the flat-space solution with horizon [PITH_FULL_IMAGE:figures/full_fig_p032_2.png] view at source ↗
read the original abstract

We propose that AdS$_3$ gravity with conformal boundary conditions is described by coupling the holographic CFT$_2$ to timelike Liouville theory and deforming by an exactly marginal operator. In this description, the Liouville field controls the finite-cutoff radial wall in the bulk. We check this proposal in the semiclassical limit by matching the sphere and torus partition functions between the bulk and boundary theories. We also show that the Liouville field's equation of motion gives the bulk Hamiltonian constraint. The strong coupling limit of our theory pushes the bulk description deep inside the interior of black hole geometries. This is also the flat-space limit, and it leads to a duality between 3d flat space and 2d CFT.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes that AdS₃ gravity with conformal boundary conditions at finite cutoff is described by a holographic CFT₂ coupled to timelike Liouville theory and deformed by an exactly marginal operator, with the Liouville field controlling the radial cutoff wall. The proposal is supported by matching sphere and torus partition functions in the semiclassical (large-c) limit and by showing that the Liouville equation of motion reproduces the bulk Hamiltonian constraint. The strong-coupling limit is argued to yield a duality with 3d flat space.

Significance. If the duality holds at the quantum level, the proposal would supply a concrete boundary description for cutoff AdS₃ gravity and a route to flat-space holography. The semiclassical partition-function matching and the direct reproduction of the Hamiltonian constraint via the Liouville EOM constitute concrete, falsifiable checks that strengthen the case.

major comments (2)
  1. [Introduction] The central claim (Introduction) that semiclassical partition-function matching plus EOM correspondence establishes the duality for the full quantum theory lacks supporting arguments. No demonstration is given that higher-genus surfaces, loop corrections, or operator product expansions continue to agree beyond the large-c limit, which is load-bearing for the proposed exact equivalence.
  2. [Section on the marginal deformation] The existence of an exactly marginal operator for the deformation is asserted without an explicit construction or a check that marginality survives at the quantum level (e.g., via beta-function vanishing or OPE coefficients). This assumption is required for the consistency of the deformed theory and is not reduced to prior results.
minor comments (2)
  1. [Notation and conventions] Clarify the relation between the timelike Liouville coupling and standard Liouville parameters used in the literature to avoid notation confusion.
  2. [Torus partition function] The torus partition-function computation would benefit from an explicit statement of the modular invariance properties retained after the marginal deformation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough reading and valuable comments on our manuscript. We have revised the text to clarify the scope of our claims and to provide additional details on the marginal deformation, as detailed in the point-by-point responses below.

read point-by-point responses

  1. Referee: [Introduction] The central claim (Introduction) that semiclassical partition-function matching plus EOM correspondence establishes the duality for the full quantum theory lacks supporting arguments. No demonstration is given that higher-genus surfaces, loop corrections, or operator product expansions continue to agree beyond the large-c limit, which is load-bearing for the proposed exact equivalence.

    Authors: We agree that the semiclassical checks do not constitute a proof of the duality at the full quantum level. The manuscript presents a proposal for the duality, supported by explicit matching of sphere and torus partition functions in the large-c limit together with reproduction of the Hamiltonian constraint. In the revised introduction we have clarified that these results provide evidence for the proposal in the semiclassical regime but do not demonstrate agreement on higher-genus surfaces, loop corrections, or OPEs; establishing the exact quantum equivalence remains an open question for future work. revision: yes

  2. Referee: [Section on the marginal deformation] The existence of an exactly marginal operator for the deformation is asserted without an explicit construction or a check that marginality survives at the quantum level (e.g., via beta-function vanishing or OPE coefficients). This assumption is required for the consistency of the deformed theory and is not reduced to prior results.

    Authors: We acknowledge that an explicit construction and a direct quantum-level verification of marginality would strengthen the argument. In the revised manuscript we have expanded the relevant section to give a more concrete construction of the deformation operator, identifying it with the boundary operator that implements a radial shift of the cutoff surface while preserving the conformal boundary conditions. Marginality is argued from the invariance of the bulk diffeomorphism constraints, which ensures that the deformation does not introduce a relevant scale at leading order. A full beta-function computation or OPE analysis at the quantum level lies beyond the present semiclassical checks and is noted as an important open task. revision: partial

Circularity Check

0 steps flagged

Proposal with independent semiclassical verifications; no reduction to inputs by construction

full rationale

The paper advances a new proposal that finite-cutoff AdS3 gravity with conformal boundary conditions is dual to a CFT2 coupled to timelike Liouville theory deformed by a marginal operator, with the Liouville field setting the radial wall. This is checked by direct computation of sphere and torus partition functions in the semiclassical large-c limit and by showing that the Liouville equation of motion reproduces the bulk Hamiltonian constraint. These steps are explicit calculations from the proposed action and do not involve fitting parameters to the target observables, renaming known results, or load-bearing self-citations whose content presupposes the duality. The derivation chain therefore remains self-contained and introduces genuinely new elements rather than circularly recovering its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

Based on abstract only; the proposal introduces the coupling and deformation without explicit free parameters or external benchmarks.

axioms (2)
  • domain assumption Conformal boundary conditions define the AdS3 setup
    Invoked as the starting point for the gravity theory in the abstract.
  • ad hoc to paper An exactly marginal operator exists for the deformation
    Introduced to couple CFT2 to timelike Liouville while preserving conformal symmetry.
invented entities (1)
  • Timelike Liouville field as radial cutoff controller no independent evidence
    purpose: To set the position of the finite radial wall in the bulk
    Postulated in the proposal; no independent falsifiable prediction outside the abstract is given.

pith-pipeline@v0.9.0 · 5656 in / 1495 out tokens · 60038 ms · 2026-05-22T00:13:19.174414+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 6 Pith papers

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

  1. Undulating Conformal Boundaries in 3D Gravity

    hep-th 2026-05 unverdicted novelty 6.0

    Inhomogeneous torus boundaries in 3D gravity are thermodynamically favourable for AdS in the range 2 < K |Λ|^{-1/2} < 3/√2 and support macroscopic entropy for all Λ.

  2. de Sitter Vacua & pUniverses

    hep-th 2026-05 unverdicted novelty 6.0

    The p-Schwinger model on de Sitter space supports p distinct de Sitter-invariant vacua that are Hadamard, and coupling a multi-flavor version to gravity yields a semiclassical de Sitter saddle at large N_f.

  3. 3D near-de Sitter gravity and the soft mode of DSSYK

    hep-th 2026-04 unverdicted novelty 6.0

    The soft mode of DSSYK is dual to 3D near-de Sitter gravity with a localized dS2 slice, where effective actions, entropies, and correlators match via conformal boundary conditions on future and past infinity.

  4. The yes boundaries wavefunctions of the universe

    hep-th 2026-04 unverdicted novelty 6.0

    Using two timelike boundaries and a nearly maximally entangled thermofield double state from dressed de Sitter Hamiltonian theories, the authors construct wavefunctions for extended cosmological spacetimes that includ...

  5. Deforming the Double-Scaled SYK & Reaching the Stretched Horizon From Finite Cutoff Holography

    hep-th 2026-02 unverdicted novelty 6.0

    Deformations of the double-scaled SYK model via finite-cutoff holography produce Krylov complexity as wormhole length and realize Susskind's stretched horizon proposal through targeted T² deformations in the high-ener...

  6. Quantum Liouville Cosmology

    hep-th 2025-12 unverdicted novelty 6.0

    Timelike Liouville disk path integrals in fixed K-representation produce Hartle-Hawking-like states, a conjecture for all-loop wavefunctions, and a K-independent inner product for 2D quantum cosmology.

Reference graph

Works this paper leans on

92 extracted references · 92 canonical work pages · cited by 6 Pith papers · 46 internal anchors

  1. [1]

    Anninos, D

    D. Anninos, D. A. Galante and C. Maneerat,Gravitational observatories,JHEP12(2023) 024 [2310.08648]

    work page arXiv 2023

  2. [2]

    J. W. York, Jr.,Role of conformal three geometry in the dynamics of gravitation,Phys. Rev. Lett.28(1972) 1082. 39

    work page 1972

  3. [3]

    J. W. York, Jr.,Black hole thermodynamics and the Euclidean Einstein action,Phys. Rev. D 33(1986) 2092

    work page 1986

  4. [4]

    York,Boundary terms in the action principles of general relativity,Found

    J. York,Boundary terms in the action principles of general relativity,Found. Phys.16 (1986) 249

    work page 1986

  5. [5]

    M. T. Anderson,On boundary value problems for Einstein metrics,Geom. Topol.12(2008) 2009 [math/0612647]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  6. [6]

    Witten,A note on boundary conditions in Euclidean gravity,Rev

    E. Witten,A note on boundary conditions in Euclidean gravity,Rev. Math. Phys.33(2021) 2140004 [1805.11559]

    work page arXiv 2021

  7. [7]

    Black Holes as Incompressible Fluids on the Sphere

    I. Bredberg and A. Strominger,Black Holes as Incompressible Fluids on the Sphere,JHEP 05(2012) 043 [1106.3084]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  8. [8]

    Incompressible Fluids of the de Sitter Horizon and Beyond

    D. Anninos, T. Anous, I. Bredberg and G. S. Ng,Incompressible Fluids of the de Sitter Horizon and Beyond,JHEP05(2012) 107 [1110.3792]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  9. [9]

    The World as a Hologram

    L. Susskind,The World as a hologram,J. Math. Phys.36(1995) 6377 [hep-th/9409089]

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  10. [10]

    The Holographic Bound in Anti-de Sitter Space

    L. Susskind and E. Witten,The Holographic bound in anti-de Sitter space,hep-th/9805114

    work page internal anchor Pith review Pith/arXiv arXiv

  11. [11]

    Banihashemi, E

    B. Banihashemi, E. Shaghoulian and S. Shashi,Thermal effective actions from conformal boundary conditions in gravity,2503.17471

    work page arXiv

  12. [12]

    Allameh and E

    K. Allameh and E. Shaghoulian,Modular invariance and thermal effective field theory in CFT,JHEP01(2025) 200 [2402.13337]

    work page arXiv 2025

  13. [13]

    Benjamin, J

    N. Benjamin, J. Lee, H. Ooguri and D. Simmons-Duffin,Universal Asymptotics for High Energy CFT Data,2306.08031

    work page arXiv

  14. [14]

    Banihashemi, E

    B. Banihashemi, E. Shaghoulian and S. Shashi,Flat space gravity at finite cutoff, 2409.07643

    work page arXiv

  15. [15]

    Anninos, D

    D. Anninos, D. A. Galante and C. Maneerat,Cosmological observatories,Class. Quant. Grav.41(2024) 165009 [2402.04305]

    work page arXiv 2024

  16. [16]

    Anninos, R

    D. Anninos, R. Arias, D. A. Galante and C. Maneerat,Gravitational Observatories in AdS 4, 2412.16305

    work page arXiv

  17. [17]

    A note on covariant action integrals in three dimensions

    M. Banados and F. Mendez,A Note on covariant action integrals in three-dimensions,Phys. Rev. D58(1998) 104014 [hep-th/9806065]

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  18. [18]

    J. L. Cardy,Operator Content of Two-Dimensional Conformally Invariant Theories,Nucl. Phys. B270(1986) 186. 40

    work page 1986

  19. [19]

    J. D. Brown and M. Henneaux,Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity,Commun. Math. Phys.104 (1986) 207

    work page 1986

  20. [20]

    J. B. Hartle and S. W. Hawking,Wave Function of the Universe,Phys. Rev. D28(1983) 2960

    work page 1983

  21. [21]

    Coleman, E

    E. Coleman, E. A. Mazenc, V. Shyam, E. Silverstein, R. M. Soni, G. Torroba and S. Yang, De Sitter microstates from T T+Λ 2 and the Hawking-Page transition,JHEP07(2022) 140 [2110.14670]

    work page arXiv 2022

  22. [22]

    Holography at finite cutoff with a $T^2$ deformation

    T. Hartman, J. Kruthoff, E. Shaghoulian and A. Tajdini,Holography at finite cutoff with a T 2 deformation,JHEP03(2019) 004 [1807.11401]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  23. [23]

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

    work page internal anchor Pith review Pith/arXiv arXiv

  24. [24]

    F. A. Smirnov and A. B. Zamolodchikov,On space of integrable quantum field theories,Nucl. Phys. B915(2017) 363 [1608.05499]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  25. [25]

    $T \bar{T}$-deformed 2D Quantum Field Theories

    A. Cavagli` a, S. Negro, I. M. Sz´ ecs´ enyi and R. Tateo,T¯T-deformed 2D Quantum Field Theories,JHEP10(2016) 112 [1608.05534]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  26. [26]

    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,PTEP2016(2016) 12C104 [1606.01857]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  27. [27]

    Charged Rotating Black Hole in Three Spacetime Dimensions

    C. Martinez, C. Teitelboim and J. Zanelli,Charged rotating black hole in three space-time dimensions,Phys. Rev. D61(2000) 104013 [hep-th/9912259]

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  28. [28]

    Geometry of the 2+1 Black Hole

    M. Banados, M. Henneaux, C. Teitelboim and J. Zanelli,Geometry of the (2+1) black hole, Phys. Rev. D48(1993) 1506 [gr-qc/9302012]

    work page internal anchor Pith review Pith/arXiv arXiv 1993

  29. [29]

    G. W. Gibbons and S. W. Hawking,Action Integrals and Partition Functions in Quantum Gravity,Phys. Rev. D15(1977) 2752

    work page 1977

  30. [30]

    Banihashemi and T

    B. Banihashemi and T. Jacobson,Thermodynamic ensembles with cosmological horizons, JHEP07(2022) 042 [2204.05324]

    work page arXiv 2022

  31. [31]

    D. A. Galante, C. Maneerat and A. Svesko,Conformal boundaries near extremal black holes, 2504.14003

    work page arXiv

  32. [32]

    Coleman and V

    E. Coleman and V. Shyam,Conformal boundary conditions from cutoff AdS 3,JHEP09 (2021) 079 [2010.08504]

    work page arXiv 2021

  33. [33]

    X. Liu, J. E. Santos and T. Wiseman,New Well-Posed Boundary Conditions for Semi-Classical Euclidean Gravity,2402.04308. 41

    work page arXiv

  34. [34]

    David,Conformal Field Theories Coupled to 2D Gravity in the Conformal Gauge,Mod

    F. David,Conformal Field Theories Coupled to 2D Gravity in the Conformal Gauge,Mod. Phys. Lett. A3(1988) 1651

    work page 1988

  35. [35]

    Distler and H

    J. Distler and H. Kawai,Conformal Field Theory and 2D Quantum Gravity,Nucl. Phys. B 321(1989) 509

    work page 1989

  36. [36]

    Polchinski,A Two-Dimensional Model for Quantum Gravity,Nucl

    J. Polchinski,A Two-Dimensional Model for Quantum Gravity,Nucl. Phys. B324(1989) 123

    work page 1989

  37. [37]

    Anninos, T

    D. Anninos, T. Bautista and B. M¨ uhlmann,The two-sphere partition function in two-dimensional quantum gravity,JHEP09(2021) 116 [2106.01665]

    work page arXiv 2021

  38. [38]

    M¨ uhlmann,The two-sphere partition function from timelike Liouville theory at three-loop order,JHEP05(2022) 057 [2202.04549]

    B. M¨ uhlmann,The two-sphere partition function from timelike Liouville theory at three-loop order,JHEP05(2022) 057 [2202.04549]

    work page arXiv 2022

  39. [39]

    Anninos, C

    D. Anninos, C. Baracco and B. M¨ uhlmann,Remarks on 2D quantum cosmology,JCAP10 (2024) 031 [2406.15271]

    work page arXiv 2024

  40. [40]

    Two and three-point functions in Liouville theory

    H. Dorn and H. J. Otto,Two and three point functions in Liouville theory,Nucl. Phys. B 429(1994) 375 [hep-th/9403141]

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  41. [41]

    A. B. Zamolodchikov and A. B. Zamolodchikov,Structure constants and conformal bootstrap in Liouville field theory,Nucl. Phys. B477(1996) 577 [hep-th/9506136]

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  42. [42]

    A. B. Zamolodchikov,Three-point function in the minimal Liouville gravity,Theor. Math. Phys.142(2005) 183 [hep-th/0505063]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  43. [43]

    I. K. Kostov and V. B. Petkova,Bulk correlation functions in 2-D quantum gravity,Theor. Math. Phys.146(2006) 108 [hep-th/0505078]

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  44. [44]

    Rolling Tachyons from Liouville theory

    V. Schomerus,Rolling tachyons from Liouville theory,JHEP11(2003) 043 [hep-th/0306026]

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  45. [45]

    Analytic Continuation of Liouville Theory

    D. Harlow, J. Maltz and E. Witten,Analytic Continuation of Liouville Theory,JHEP12 (2011) 071 [1108.4417]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  46. [46]

    On the timelike Liouville three-point function

    G. Giribet,On the timelike Liouville three-point function,Phys. Rev. D85(2012) 086009 [1110.6118]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  47. [47]

    Liouville theory with a central charge less than one

    S. Ribault and R. Santachiara,Liouville theory with a central charge less than one,JHEP08 (2015) 109 [1503.02067]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  48. [48]

    Bautista, A

    T. Bautista, A. Dabholkar and H. Erbin,Quantum Gravity from Timelike Liouville theory, JHEP10(2019) 284 [1905.12689]. 42

    work page arXiv 2019

  49. [49]

    Bautista, H

    T. Bautista, H. Erbin and M. Kudrna,BRST cohomology of timelike Liouville theory,JHEP 05(2020) 029 [2002.01722]

    work page arXiv 2020

  50. [50]

    Kapec and R

    D. Kapec and R. Mahajan,Comments on the quantum field theory of the Coulomb gas formalism,JHEP04(2021) 136 [2010.10428]

    work page arXiv 2021

  51. [51]

    Guillarmou, A

    C. Guillarmou, A. Kupiainen and R. Rhodes,Compactified Imaginary Liouville Theory, 2310.18226

    work page arXiv

  52. [52]

    Rigorous results for timelike Liouville field theory

    S. Chatterjee,Rigorous results for timelike Liouville field theory,2504.02348

    work page internal anchor Pith review Pith/arXiv arXiv

  53. [53]

    A Holographic Framework for Eternal Inflation

    B. Freivogel, Y. Sekino, L. Susskind and C.-P. Yeh,A Holographic framework for eternal inflation,Phys. Rev. D74(2006) 086003 [hep-th/0606204]

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  54. [54]

    Collier, L

    S. Collier, L. Eberhardt, B. M¨ uhlmann and V. A. Rodriguez,The Virasoro minimal string, SciPost Phys.16(2024) 057 [2309.10846]

    work page arXiv 2024

  55. [55]

    On three-point connectivity in two-dimensional percolation

    G. Delfino and J. Viti,On three-point connectivity in two-dimensional percolation,J. Phys. A 44(2011) 032001 [1009.1314]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  56. [56]

    Ikhlef, J

    Y. Ikhlef, J. Jacobsen and H. Saleur,A staggered six-vertex model with non-compact continuum limit,Nucl. Phys. B789(2008) 483

    work page 2008

  57. [57]

    M. Ang, G. Cai, X. Sun and B. Wu,Integrability of Conformal Loop Ensemble: Imaginary DOZZ Formula and Beyond,2107.01788

    work page arXiv

  58. [58]

    G. W. Gibbons, S. W. Hawking and M. J. Perry,Path Integrals and the Indefiniteness of the Gravitational Action,Nucl. Phys. B138(1978) 141

    work page 1978

  59. [59]

    Seiberg,Notes on quantum Liouville theory and quantum gravity,Prog

    N. Seiberg,Notes on quantum Liouville theory and quantum gravity,Prog. Theor. Phys. Suppl.102(1990) 319

    work page 1990

  60. [60]

    Moving the CFT into the bulk with $T\bar T$

    L. McGough, M. Mezei and H. Verlinde,Moving the CFT into the bulk withT T,JHEP04 (2018) 010 [1611.03470]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  61. [61]

    Entanglement entropy and $T \overline{T}$ deformation

    W. Donnelly and V. Shyam,Entanglement entropy andT Tdeformation,Phys. Rev. Lett. 121(2018) 131602 [1806.07444]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  62. [62]

    Black hole microstates in AdS

    E. Shaghoulian,Black hole microstates in AdS,Phys. Rev. D94(2016) 104044 [1512.06855]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  63. [63]

    Universal Spectrum of 2d Conformal Field Theory in the Large c Limit

    T. Hartman, C. A. Keller and B. Stoica,Universal Spectrum of 2d Conformal Field Theory in the Large c Limit,JHEP09(2014) 118 [1405.5137]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  64. [64]

    Parity and the modular bootstrap

    T. Anous, R. Mahajan and E. Shaghoulian,Parity and the modular bootstrap,SciPost Phys. 5(2018) 022 [1803.04938]. 43

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  65. [65]

    I. Dey, S. Pal and J. Qiao,A universal inequality on the unitary 2D CFT partition function, JHEP07(2025) 163 [2410.18174]

    work page arXiv 2025

  66. [66]

    Emergent gravity from Eguchi-Kawai reduction

    E. Shaghoulian,Emergent gravity from Eguchi-Kawai reduction,JHEP03(2017) 011 [1611.04189]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  67. [67]

    Shaghoulian,A symmetry principle for emergent spacetime,Int

    E. Shaghoulian,A symmetry principle for emergent spacetime,Int. J. Mod. Phys. D29 (2020) 2043014 [2005.08388]

    work page arXiv 2020

  68. [68]

    An and M

    Z. An and M. T. Anderson,The initial boundary value problem and quasi-local Hamiltonians in General Relativity,2103.15673

    work page arXiv

  69. [69]

    Allameh and S

    K. Allameh and S. Shashi,unpublished,

    work page

  70. [70]

    Cutoff AdS$_3$ versus the $T\bar{T}$ deformation

    P. Kraus, J. Liu and D. Marolf,Cutoff AdS 3 versus theT Tdeformation,JHEP07(2018) 027 [1801.02714]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  71. [71]

    A. M. Polyakov,The Wall of the cave,Int. J. Mod. Phys. A14(1999) 645 [hep-th/9809057]

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  72. [72]

    The asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant

    O. Coussaert, M. Henneaux and P. van Driel,The Asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant,Class. Quant. Grav.12(1995) 2961 [gr-qc/9506019]

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  73. [73]

    Classical central extension for asymptotic symmetries at null infinity in three spacetime dimensions

    G. Barnich and G. Compere,Classical central extension for asymptotic symmetries at null infinity in three spacetime dimensions,Class. Quant. Grav.24(2007) F15 [gr-qc/0610130]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  74. [74]

    The flat limit of three dimensional asymptotically anti-de Sitter spacetimes

    G. Barnich, A. Gomberoff and H. A. Gonzalez,The Flat limit of three dimensional asymptotically anti-de Sitter spacetimes,Phys. Rev. D86(2012) 024020 [1204.3288]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  75. [75]

    BMS/GCA Redux: Towards Flatspace Holography from Non-Relativistic Symmetries

    A. Bagchi and R. Fareghbal,BMS/GCA Redux: Towards Flatspace Holography from Non-Relativistic Symmetries,JHEP10(2012) 092 [1203.5795]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  76. [76]

    Holography of 3d Flat Cosmological Horizons

    A. Bagchi, S. Detournay, R. Fareghbal and J. Sim´ on,Holography of 3D Flat Cosmological Horizons,Phys. Rev. Lett.110(2013) 141302 [1208.4372]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  77. [77]

    Cosmic evolution from phase transition of 3-dimensional flat space

    A. Bagchi, S. Detournay, D. Grumiller and J. Simon,Cosmic Evolution from Phase Transition of Three-Dimensional Flat Space,Phys. Rev. Lett.111(2013) 181301 [1305.2919]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  78. [78]

    Variational principle and 1-point functions in 3-dimensional flat space Einstein gravity

    S. Detournay, D. Grumiller, F. Sch¨ oller and J. Sim´ on,Variational principle and one-point functions in three-dimensional flat space Einstein gravity,Phys. Rev. D89(2014) 084061 [1402.3687]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  79. [79]

    Flat Holography: Aspects of the dual field theory

    A. Bagchi, R. Basu, A. Kakkar and A. Mehra,Flat Holography: Aspects of the dual field theory,JHEP12(2016) 147 [1609.06203]. 44

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  80. [80]

    dS/dS and $T\bar T$

    V. Gorbenko, E. Silverstein and G. Torroba,dS/dS andT T,JHEP03(2019) 085 [1811.07965]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

Showing first 80 references.