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arxiv: 2501.17912 · v2 · submitted 2025-01-29 · ✦ hep-th · gr-qc

De Sitter Horizon Edge Partition Functions

Y.T. Albert Law This is my paper

Pith reviewed 2026-05-23 04:14 UTC · model grok-4.3

classification ✦ hep-th gr-qc
keywords de Sitter spacepartition functionsedge modeslinearized gravityhorizon degrees of freedomshift-symmetric fieldstensor fieldsso(d) representations
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The pith

For linearized Einstein gravity on S^{d+1}, the edge partition function receives contributions from shift-symmetric vector and scalar fields on S^{d-1}.

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

The paper establishes that one-loop path integrals on the de Sitter sphere S^{d+1} separate into a bulk thermal ideal gas term in the static patch and an edge term tied to degrees of freedom on the horizon sphere S^{d-1}. It determines the so(d) representation content of the edge partition functions for totally symmetric tensor fields of arbitrary rank, both massive and massless. In the case of linearized gravity, those edge contributions reduce to shift-symmetric vector and scalar fields on S^{d-1}. A sympathetic reader would care because the result supplies a concrete description of horizon modes that might be reinterpreted as an embedded lower-dimensional brane.

Core claim

One-loop S^{d+1} path integrals factorize into a bulk thermal ideal gas partition function in a dS_{d+1} static patch and an edge partition function associated with degrees of freedom living on S^{d-1}. For linearized Einstein gravity on S^{d+1}, the edge partition function receives contributions from shift-symmetric vector and scalar fields on S^{d-1}, suggesting a possible interpretation in terms of an embedded S^{d-1} brane. The same so(d) analysis applies to massive and massless totally symmetric tensors of any rank in d greater than or equal to 3.

What carries the argument

Edge partition function for totally symmetric tensor fields on S^{d-1}, obtained by isolating the so(d) content after bulk-edge factorization of the one-loop path integral.

If this is right

  • The edge partition function for any totally symmetric tensor is fixed once its so(d) representation content on S^{d-1} is known.
  • Linearized gravity receives edge contributions precisely from the shift-symmetric vector and scalar sectors on the horizon sphere.
  • The same edge structure holds for both massive and massless tensors in every dimension d at least 3.
  • The edge modes admit a possible reinterpretation as the degrees of freedom of an embedded S^{d-1} brane.

Where Pith is reading between the lines

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

  • The brane suggestion would imply that the horizon carries an effective lower-dimensional theory whose spectrum is exhausted by the shift-symmetric fields already identified.
  • The bulk-edge split could be applied to other maximally symmetric spaces to isolate analogous horizon contributions.
  • Computing the edge partition function for interacting or higher-spin fields would test whether the shift-symmetric pattern persists beyond the free linearized case.

Load-bearing premise

One-loop S^{d+1} path integrals factorize into a bulk thermal ideal gas partition function in a dS_{d+1} static patch and an edge partition function associated with degrees of freedom living on S^{d-1}.

What would settle it

An explicit computation of the full one-loop partition function for linearized gravity on S^{4} that fails to equal the sum of the known bulk static-patch ideal-gas term plus the edge term built from shift-symmetric vector and scalar fields on S^{3}.

Figures

Figures reproduced from arXiv: 2501.17912 by Y.T. Albert Law.

Figure 1.1
Figure 1.1. Figure 1.1: Left: Penrose diagram for dSd+1 and a static patch (highlighted in blue). The yellow dot indicates the bifurcation surface at r = ℓdS. Right: Upon the Wick rotation t → −iτ , τ ∼ τ + 2π, the static patch becomes the round sphere, with τ parametrizing the thermal circle. Interestingly, for any fields with spin s ≥ 1, (1.5) is modified by some “edge” contribution3 ZPI = Zbulk(β = 2π)Zedge (spin s ≥ 1) . (1… view at source ↗
Figure 5.1
Figure 5.1. Figure 5.1: In the brane interpretation of Zedge, ϕ a describes the deformations of the round S d−1 (left) in the Xa -direction upon embedding in S d+1 . Aµ, represented by a vector field in the right figure, describes diffeomorphisms on the sphere. While it is not clear to us at this point how to naturally incorporate Aµ and χ into the action (5.46) so that the full SO(d + 2) symmetry is nonlinearly realized, they … view at source ↗
read the original abstract

One-loop $S^{d+1}$ path integrals were shown to factorize into two parts: a bulk thermal ideal gas partition function in a $dS_{d+1}$ static patch and an edge partition function associated with degrees of freedom living on $S^{d-1}$. Here, we analyze the $\mathfrak{so}(d)$ structure of the edge partition functions for massive and massless totally symmetric tensors of arbitrary rank in any $d\geq 3$. For linearized Einstein gravity on $S^{d+1}$, we find that the edge partition function receives contributions from shift-symmetric vector and scalar fields on $S^{d-1}$, suggesting a possible interpretation in terms of an embedded $S^{d-1}$ brane.

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 / 0 minor

Summary. The manuscript analyzes the so(d) representation content of edge partition functions arising from one-loop path integrals of massive and massless totally symmetric tensor fields of arbitrary rank on S^{d+1} (d≥3). Building on a prior factorization of these path integrals into a bulk thermal ideal gas contribution in the dS_{d+1} static patch and an edge contribution associated with degrees of freedom on S^{d-1}, the paper reports that for linearized Einstein gravity the edge partition function receives contributions from shift-symmetric vector and scalar fields on S^{d-1}, suggesting a possible interpretation in terms of an embedded S^{d-1} brane.

Significance. If the factorization and representation decomposition hold, the work supplies a systematic so(d) decomposition of edge modes for tensor fields in de Sitter space, which may clarify horizon degrees of freedom and motivate brane interpretations. The extension to arbitrary rank tensors is a technical strength, though the absence of explicit derivations, error estimates, or checks against known cases for the spin-2 sector reduces immediate applicability.

major comments (2)
  1. [Abstract] Abstract: The central claim that the edge partition function for linearized Einstein gravity receives contributions specifically from shift-symmetric vector and scalar fields on S^{d-1} rests on the factorization of the one-loop S^{d+1} path integral into bulk ideal gas plus edge on S^{d-1}. The manuscript states this factorization 'were shown to factorize' but provides no re-derivation or verification for the spin-2 case, leaving the identification dependent on unexamined technical steps from prior work.
  2. [Abstract] The identification of the edge so(d) content for gravity assumes an exact bulk-edge separation. No explicit check is given against possible mixing from residual gauge modes, boundary terms in the Lichnerowicz operator, or regularization choices, which would undermine the reported shift-symmetric contributions if the separation is not exact.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments. We address the major comments point by point below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim that the edge partition function for linearized Einstein gravity receives contributions specifically from shift-symmetric vector and scalar fields on S^{d-1} rests on the factorization of the one-loop S^{d+1} path integral into bulk ideal gas plus edge on S^{d-1}. The manuscript states this factorization 'were shown to factorize' but provides no re-derivation or verification for the spin-2 case, leaving the identification dependent on unexamined technical steps from prior work.

    Authors: The factorization into bulk thermal ideal gas and edge contributions on S^{d-1} was established in our prior work for the graviton (spin-2) case. The present manuscript takes this established result as input and performs the so(d) decomposition of the resulting edge partition function for arbitrary-rank tensors. To address the concern about self-contained presentation, we will revise the manuscript to include a concise recap of the key factorization steps specific to the linearized gravity case. revision: yes

  2. Referee: [Abstract] The identification of the edge so(d) content for gravity assumes an exact bulk-edge separation. No explicit check is given against possible mixing from residual gauge modes, boundary terms in the Lichnerowicz operator, or regularization choices, which would undermine the reported shift-symmetric contributions if the separation is not exact.

    Authors: The bulk-edge separation is defined by the path-integral factorization, which incorporates gauge fixing, boundary conditions, and the Lichnerowicz operator for the graviton. The shift-symmetric vector and scalar contributions on S^{d-1} arise directly from this separation. While the current work does not repeat explicit checks for mixing or regularization artifacts (these were addressed in the derivation of the factorization), we can add a clarifying paragraph referencing how residual gauge modes are excluded from the edge sector. revision: partial

Circularity Check

1 steps flagged

Factorization cited from prior work; new edge decomposition is independent

specific steps
  1. self citation load bearing [Abstract]
    "One-loop $S^{d+1}$ path integrals were shown to factorize into two parts: a bulk thermal ideal gas partition function in a $dS_{d+1}$ static patch and an edge partition function associated with degrees of freedom living on $S^{d-1}$."

    The identification that the edge piece for linearized Einstein gravity receives contributions from shift-symmetric fields on $S^{d-1}$ presupposes the exact bulk/edge split; this split is imported via citation without re-derivation or check for the spin-2 case in the present work.

full rationale

The paper cites a prior result for the bulk-edge factorization of the one-loop path integral and then performs a direct representation-theoretic decomposition of the edge piece for symmetric tensors. No quantities are fitted to data, no self-definitional loops appear in the so(d) content calculation, and the central new claim (shift-symmetric vector/scalar contributions for gravity) follows from the decomposition rather than reducing to the cited input by construction. This is a standard minor self-citation on an enabling assumption, not load-bearing circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on the factorization of the path integral (a domain assumption from prior work) and introduces a brane interpretation without independent evidence.

axioms (1)
  • domain assumption One-loop S^{d+1} path integrals factorize into bulk thermal ideal gas and edge partition functions on S^{d-1}
    Explicitly stated as previously shown in the abstract opening sentence.
invented entities (1)
  • embedded S^{d-1} brane no independent evidence
    purpose: Suggested physical interpretation of the edge degrees of freedom in the gravity case
    Presented only as a possible interpretation; no independent evidence or falsifiable prediction is supplied in the abstract.

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Forward citations

Cited by 4 Pith papers

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  2. de Sitter Vacua & pUniverses

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  3. Localization and anomalous reference frames in gravity

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  4. Gravitons on Nariai Edges

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    The one-loop graviton path integral on S² × S^{d-1} factorizes into a bulk thermal graviton gas partition function in Nariai geometry and an edge contribution from shift-symmetric fields on S^{d-1}.

Reference graph

Works this paper leans on

176 extracted references · 176 canonical work pages · cited by 4 Pith papers · 64 internal anchors

  1. [1]

    Quantum de Sitter horizon entropy from quasicanonical bulk, edge, sphere and topological string partition functions,

    D. Anninos, F. Denef, Y. T. A. Law, and Z. Sun, “Quantum de Sitter horizon entropy from quasicanonical bulk, edge, sphere and topological string partition functions,” JHEP 01 (2022) 088, arXiv:2009.12464 [hep-th]

    work page arXiv 2022

  2. [2]

    A compendium of sphere path integrals,

    Y. T. A. Law, “A compendium of sphere path integrals,” JHEP 21 (2020) 213, arXiv:2012.06345 [hep-th]

    work page arXiv 2020

  3. [3]

    Partition functions of p-forms from Harish-Chandra characters,

    J. R. David and J. Mukherjee, “Partition functions of p-forms from Harish-Chandra characters,” JHEP 09 (2021) 094, arXiv:2105.03662 [hep-th]

    work page arXiv 2021

  4. [4]

    Three-dimensional de Sitter horizon thermodynamics,

    D. Anninos and E. Harris, “Three-dimensional de Sitter horizon thermodynamics,” JHEP 10 (2021) 091, arXiv:2106.13832 [hep-th] . 58

    work page arXiv 2021

  5. [5]

    The two-sphere partition function in two-dimensional quantum gravity,

    D. Anninos, T. Bautista, and B. M¨ uhlmann, “The two-sphere partition function in two-dimensional quantum gravity,” JHEP 09 (2021) 116, arXiv:2106.01665 [hep-th]

    work page arXiv 2021

  6. [6]

    The semiclassical gravitational path integral and random matrices (toward a microscopic picture of a dS 2 universe),

    D. Anninos and B. M¨ uhlmann, “The semiclassical gravitational path integral and random matrices (toward a microscopic picture of a dS 2 universe),” JHEP 12 (2021) 206, arXiv:2111.05344 [hep-th]

    work page arXiv 2021

  7. [7]

    Characters, quasinormal modes, and Schwinger pairs in dS2 with flux,

    M. Grewal and K. Parmentier, “Characters, quasinormal modes, and Schwinger pairs in dS2 with flux,” arXiv:2112.07630 [hep-th]

    work page arXiv

  8. [8]

    The two-sphere partition function from timelike Liouville theory at three-loop order,

    B. M¨ uhlmann, “The two-sphere partition function from timelike Liouville theory at three-loop order,” JHEP 05 (2022) 057, arXiv:2202.04549 [hep-th]

    work page arXiv 2022

  9. [9]

    Microscopics of de Sitter Entropy from Precision Holography,

    N. Bobev, T. Hertog, J. Hong, J. Karlsson, and V. Reys, “Microscopics of de Sitter Entropy from Precision Holography,” Phys. Rev. X 13 no. 4, (2023) 041056, arXiv:2211.05907 [hep-th]

    work page arXiv 2023

  10. [10]

    Keeping matter in the loop in dS 3 quantum gravity,

    A. Castro, I. Coman, J. R. Fliss, and C. Zukowski, “Keeping matter in the loop in dS 3 quantum gravity,” JHEP 07 (2023) 120, arXiv:2302.12281 [hep-th]

    work page arXiv 2023

  11. [11]

    Coupling Fields to 3D Quantum Gravity via Chern-Simons Theory,

    A. Castro, I. Coman, J. R. Fliss, and C. Zukowski, “Coupling Fields to 3D Quantum Gravity via Chern-Simons Theory,” Phys. Rev. Lett. 131 no. 17, (2023) 171602, arXiv:2304.02668 [hep-th]

    work page arXiv 2023

  12. [12]

    Spinning up the spool: Massive spinning fields in 3d quantum gravity,

    R. Bourne, A. Castro, and J. R. Fliss, “Spinning up the spool: Massive spinning fields in 3d quantum gravity,” arXiv:2407.09608 [hep-th]

    work page arXiv

  13. [13]

    Quantum de sitter entropy and sphere partition functions: A-hypergeometric approach to higher loop corrections,

    B. Bandaru, “Quantum de sitter entropy and sphere partition functions: A-hypergeometric approach to higher loop corrections,” 2024. https://arxiv.org/abs/2411.16636

    work page arXiv 2024

  14. [14]

    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. D 15 (1977) 2752–2756

    work page 1977

  15. [15]

    T T + Λ 2 deformed CFT on the stretched dS 3 horizon,

    V. Shyam, “T T + Λ 2 deformed CFT on the stretched dS 3 horizon,” JHEP 04 (2022) 052, arXiv:2106.10227 [hep-th]

    work page arXiv 2022

  16. [16]

    De Sitter microstates from T T + Λ2 and the Hawking-Page transition,

    E. Coleman, E. A. Mazenc, V. Shyam, E. Silverstein, R. M. Soni, G. Torroba, and S. Yang, “De Sitter microstates from T T + Λ2 and the Hawking-Page transition,” JHEP 07 (2022) 140, arXiv:2110.14670 [hep-th]

    work page arXiv 2022

  17. [17]

    Infinite Temperature is Not So Infinite: The Many Temperatures of de Sitter Space,

    A. A. Rahman and L. Susskind, “Infinite Temperature is Not So Infinite: The Many Temperatures of de Sitter Space,” arXiv:2401.08555 [hep-th]

    work page arXiv

  18. [18]

    On infinitesimal operators of irreducible representations of the Lorentz group of n-th order,

    T. Hirai, “On irreducible representations of the Lorentz group of n-th order,” Proceedings of the Japan Academy 38 no. 6, (1962) 258 – 262. https://doi.org/10.3792/pja/1195523378. 59

    work page doi:10.3792/pja/1195523378 1962

  19. [19]

    On infinitesimal operators of irreducible representations of the Lorentz group of n-th order,

    T. Hirai, “On infinitesimal operators of irreducible representations of the Lorentz group of n-th order,” Proceedings of the Japan Academy 38 no. 3, (1962) 83 – 87. https://doi.org/10.3792/pja/1195523460

    work page doi:10.3792/pja/1195523460 1962

  20. [20]

    The characters of semisimple lie groups,

    Harish-Chandra, “The characters of semisimple lie groups,” Transactions of the American Mathematical Society 83 no. 1, (1956) 98–163. http://www.jstor.org/stable/1992907

    work page arXiv 1956

  21. [21]

    Invariant eigendistributions on semisimple lie groups,

    Harish-Chandra, “Invariant eigendistributions on semisimple lie groups,” Bulletin of the American Mathematical Society 69 no. 1, (1963) 117 – 123. https://doi.org/

    work page 1963

  22. [22]

    The characters of irreducible representations of the Lorentz group of n-th order,

    T. Hirai, “The characters of irreducible representations of the Lorentz group of n-th order,” Proceedings of the Japan Academy 41 no. 7, (1965) 526 – 531. https://doi.org/10.3792/pja/1195522333

    work page doi:10.3792/pja/1195522333 1965

  23. [23]

    Real-time observables in de Sitter thermodynamics,

    M. Grewal and Y. T. A. Law, “Real-time observables in de Sitter thermodynamics,” arXiv:2403.06006 [hep-th]

    work page arXiv

  24. [24]

    Grewal, Y

    M. Grewal, Y. T. A. Law, and V. Lochab , in preparation

    work page

  25. [25]

    Black hole scattering and partition functions,

    Y. T. A. Law and K. Parmentier, “Black hole scattering and partition functions,” JHEP 10 (2022) 039, arXiv:2207.07024 [hep-th]

    work page arXiv 2022

  26. [26]

    Characters, Quasinormal Modes, and Quantum de Sitter Thermodynamics,

    Y. T. A. Law, “Characters, Quasinormal Modes, and Quantum de Sitter Thermodynamics,” in CORFU2022: 22th Hellenic School and Workshops on Elementary Particle Physics and Gravity. 4, 2023. arXiv:2304.01471 [hep-th]

    work page arXiv 2023

  27. [27]

    Notes on gauge fields and discrete series representations in de Sitter spacetimes,

    A. Rios Fukelman, M. Semp´ e, and G. A. Silva, “Notes on gauge fields and discrete series representations in de Sitter spacetimes,” JHEP 01 (2024) 011, arXiv:2310.14955 [hep-th]

    work page arXiv 2024

  28. [28]

    Dynamical edge modes and entanglement in Maxwell theory,

    A. Ball, Y. T. A. Law, and G. Wong, “Dynamical edge modes and entanglement in Maxwell theory,” JHEP 09 (2024) 032, arXiv:2403.14542 [hep-th]

    work page arXiv 2024

  29. [29]

    Entanglement entropy and the boundary action of edge modes,

    J. Mukherjee, “Entanglement entropy and the boundary action of edge modes,” arXiv:2310.14690 [hep-th]

    work page arXiv

  30. [30]

    Dynamical Edge Modes in p-form Gauge Theories,

    A. Ball and Y. T. A. Law, “Dynamical Edge Modes in p-form Gauge Theories,” arXiv:2411.02555 [hep-th]

    work page arXiv

  31. [31]

    Black Hole Entropy and Entropy of Entanglement

    D. N. Kabat, “Black hole entropy and entropy of entanglement,” Nucl. Phys. B 453 (1995) 281–299, arXiv:hep-th/9503016

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  32. [32]

    Decomposition of entanglement entropy in lattice gauge theory

    W. Donnelly, “Decomposition of entanglement entropy in lattice gauge theory,” Phys. Rev. D 85 (2012) 085004, arXiv:1109.0036 [hep-th] . 60

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  33. [33]

    Do gauge fields really contribute negatively to black hole entropy?

    W. Donnelly and A. C. Wall, “Do gauge fields really contribute negatively to black hole entropy?,” Phys. Rev. D 86 (2012) 064042, arXiv:1206.5831 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  34. [34]

    Entanglement and Thermal Entropy of Gauge Fields

    C. Eling, Y. Oz, and S. Theisen, “Entanglement and Thermal Entropy of Gauge Fields,” JHEP 11 (2013) 019, arXiv:1308.4964 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  35. [35]

    Notes on Entanglement in Abelian Gauge Theories

    D. Radicevic, “Notes on Entanglement in Abelian Gauge Theories,” arXiv:1404.1391 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv

  36. [36]

    Entanglement entropy and nonabelian gauge symmetry

    W. Donnelly, “Entanglement entropy and nonabelian gauge symmetry,” Class. Quant. Grav. 31 no. 21, (2014) 214003, arXiv:1406.7304 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  37. [37]

    Entanglement entropy of electromagnetic edge modes

    W. Donnelly and A. C. Wall, “Entanglement entropy of electromagnetic edge modes,” Phys. Rev. Lett. 114 no. 11, (2015) 111603, arXiv:1412.1895 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  38. [38]

    Central Charge and Entangled Gauge Fields

    K.-W. Huang, “Central Charge and Entangled Gauge Fields,” Phys. Rev. D 92 no. 2, (2015) 025010, arXiv:1412.2730 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  39. [39]

    On The Entanglement Entropy For Gauge Theories

    S. Ghosh, R. M. Soni, and S. P. Trivedi, “On The Entanglement Entropy For Gauge Theories,” JHEP 09 (2015) 069, arXiv:1501.02593 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  40. [40]

    Revisiting Entanglement Entropy of Lattice Gauge Theories

    L.-Y. Hung and Y. Wan, “Revisiting Entanglement Entropy of Lattice Gauge Theories,” JHEP 04 (2015) 122, arXiv:1501.04389 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  41. [41]

    On the definition of entanglement entropy in lattice gauge theories

    S. Aoki, T. Iritani, M. Nozaki, T. Numasawa, N. Shiba, and H. Tasaki, “On the definition of entanglement entropy in lattice gauge theories,” JHEP 06 (2015) 187, arXiv:1502.04267 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  42. [42]

    Geometric entropy and edge modes of the electromagnetic field

    W. Donnelly and A. C. Wall, “Geometric entropy and edge modes of the electromagnetic field,” Phys. Rev. D 94 no. 10, (2016) 104053, arXiv:1506.05792 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  43. [43]

    Entanglement in Weakly Coupled Lattice Gauge Theories

    D. Radiˇ cevi´ c, “Entanglement in Weakly Coupled Lattice Gauge Theories,”JHEP 04 (2016) 163, arXiv:1509.08478 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  44. [44]

    Entanglement Entropy of U(1) Quantum Spin Liquids

    M. Pretko and T. Senthil, “Entanglement entropy of U(1) quantum spin liquids,” Phys. Rev. B 94 no. 12, (2016) 125112, arXiv:1510.03863 [cond-mat.str-el]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  45. [45]

    Aspects of Entanglement Entropy for Gauge Theories

    R. M. Soni and S. P. Trivedi, “Aspects of Entanglement Entropy for Gauge Theories,” JHEP 01 (2016) 136, arXiv:1510.07455 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  46. [46]

    A note on electromagnetic edge modes

    F. Zuo, “A note on electromagnetic edge modes,” arXiv:1601.06910 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv

  47. [47]

    Entanglement Entropy in (3+1)-d Free $U(1)$ Gauge Theory

    R. M. Soni and S. P. Trivedi, “Entanglement entropy in (3 + 1)-d free U(1) gauge theory,” JHEP 02 (2017) 101, arXiv:1608.00353 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  48. [48]

    On entanglement entropy in non-Abelian lattice gauge theory and 3D quantum gravity

    C. Delcamp, B. Dittrich, and A. Riello, “On entanglement entropy in non-Abelian lattice gauge theory and 3D quantum gravity,” JHEP 11 (2016) 102, arXiv:1609.04806 [hep-th]. 61

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  49. [49]

    Gauge-invariant Variables and Entanglement Entropy

    A. Agarwal, D. Karabali, and V. P. Nair, “Gauge-invariant Variables and Entanglement Entropy,” Phys. Rev. D 96 no. 12, (2017) 125008, arXiv:1701.00014 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  50. [50]

    Edge State Quantization: Vector Fields in Rindler

    A. Blommaert, T. G. Mertens, H. Verschelde, and V. I. Zakharov, “Edge State Quantization: Vector Fields in Rindler,” JHEP 08 (2018) 196, arXiv:1801.09910 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  51. [51]

    Edge Dynamics from the Path Integral: Maxwell and Yang-Mills

    A. Blommaert, T. G. Mertens, and H. Verschelde, “Edge dynamics from the path integral — Maxwell and Yang-Mills,” JHEP 11 (2018) 080, arXiv:1804.07585 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  52. [52]

    Electromagnetic duality and central charge

    L. Freidel and D. Pranzetti, “Electromagnetic duality and central charge,” Phys. Rev. D 98 no. 11, (2018) 116008, arXiv:1806.03161 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  53. [53]

    On the Quantum Structure of a Black Hole,

    G. ’t Hooft, “On the Quantum Structure of a Black Hole,” Nucl. Phys. B 256 (1985) 727–745

    work page 1985

  54. [54]

    Local subsystems in gauge theory and gravity

    W. Donnelly and L. Freidel, “Local subsystems in gauge theory and gravity,” JHEP 09 (2016) 102, arXiv:1601.04744 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  55. [55]

    Edge modes and corner ambiguities in 3d Chern-Simons theory and gravity

    M. Geiller, “Edge modes and corner ambiguities in 3d Chern–Simons theory and gravity,” Nucl. Phys. B 924 (2017) 312–365, arXiv:1703.04748 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  56. [56]

    Local phase space and edge modes for diffeomorphism-invariant theories

    A. J. Speranza, “Local phase space and edge modes for diffeomorphism-invariant theories,” JHEP 02 (2018) 021, arXiv:1706.05061 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  57. [57]

    Lorentz-diffeomorphism edge modes in 3d gravity

    M. Geiller, “Lorentz-diffeomorphism edge modes in 3d gravity,” JHEP 02 (2018) 029, arXiv:1712.05269 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  58. [58]

    Gravitational edge modes: from Kac–Moody charges to Poincar´ e networks,

    L. Freidel, E. R. Livine, and D. Pranzetti, “Gravitational edge modes: from Kac–Moody charges to Poincar´ e networks,”Class. Quant. Grav. 36 no. 19, (2019) 195014, arXiv:1906.07876 [hep-th]

    work page arXiv 2019

  59. [59]

    Gravity Edges Modes and Hayward Term,

    T. Takayanagi and K. Tamaoka, “Gravity Edges Modes and Hayward Term,” JHEP 02 (2020) 167, arXiv:1912.01636 [hep-th]

    work page arXiv 2020

  60. [60]

    Edge modes of gravity. Part I. Corner potentials and charges,

    L. Freidel, M. Geiller, and D. Pranzetti, “Edge modes of gravity. Part I. Corner potentials and charges,” JHEP 11 (2020) 026, arXiv:2006.12527 [hep-th]

    work page arXiv 2020

  61. [61]

    Edge modes of gravity. Part II. Corner metric and Lorentz charges,

    L. Freidel, M. Geiller, and D. Pranzetti, “Edge modes of gravity. Part II. Corner metric and Lorentz charges,” JHEP 11 (2020) 027, arXiv:2007.03563 [hep-th]

    work page arXiv 2020

  62. [62]

    Edge modes of gravity. Part III. Corner simplicity constraints,

    L. Freidel, M. Geiller, and D. Pranzetti, “Edge modes of gravity. Part III. Corner simplicity constraints,” JHEP 01 (2021) 100, arXiv:2007.12635 [hep-th]

    work page arXiv 2021

  63. [63]

    Gravitational edge modes, coadjoint orbits, and hydrodynamics,

    W. Donnelly, L. Freidel, S. F. Moosavian, and A. J. Speranza, “Gravitational edge modes, coadjoint orbits, and hydrodynamics,” JHEP 09 (2021) 008, arXiv:2012.10367 [hep-th] . 62

    work page arXiv 2021

  64. [64]

    Isolated surfaces and symmetries of gravity,

    L. Ciambelli and R. G. Leigh, “Isolated surfaces and symmetries of gravity,” Phys. Rev. D 104 no. 4, (2021) 046005, arXiv:2104.07643 [hep-th]

    work page arXiv 2021

  65. [65]

    Edge modes as reference frames and boundary actions from post-selection,

    S. Carrozza and P. A. Hoehn, “Edge modes as reference frames and boundary actions from post-selection,” JHEP 02 (2022) 172, arXiv:2109.06184 [hep-th]

    work page arXiv 2022

  66. [66]

    Embeddings and Integrable Charges for Extended Corner Symmetry,

    L. Ciambelli, R. G. Leigh, and P.-C. Pai, “Embeddings and Integrable Charges for Extended Corner Symmetry,” Phys. Rev. Lett. 128 (2022) , arXiv:2111.13181 [hep-th]

    work page arXiv 2022

  67. [67]

    Edge modes as dynamical frames: charges from post-selection in generally covariant theories,

    S. Carrozza, S. Eccles, and P. A. Hoehn, “Edge modes as dynamical frames: charges from post-selection in generally covariant theories,” SciPost Phys. 17 no. 2, (2024) 048, arXiv:2205.00913 [hep-th]

    work page arXiv 2024

  68. [68]

    Universal corner symmetry and the orbit method for gravity,

    L. Ciambelli and R. G. Leigh, “Universal corner symmetry and the orbit method for gravity,” Nucl. Phys. B 986 (2023) 116053, arXiv:2207.06441 [hep-th]

    work page arXiv 2023

  69. [69]

    A proposal for 3d quantum gravity and its bulk factorization,

    T. G. Mertens, J. Sim´ on, and G. Wong, “A proposal for 3d quantum gravity and its bulk factorization,” JHEP 06 (2023) 134, arXiv:2210.14196 [hep-th]

    work page arXiv 2023

  70. [70]

    A note on the bulk interpretation of the quantum extremal surface formula,

    G. Wong, “A note on the bulk interpretation of the quantum extremal surface formula,” JHEP 04 (2024) 024, arXiv:2212.03193 [hep-th]

    work page arXiv 2024

  71. [71]

    Matrix Quantization of Gravitational Edge Modes,

    W. Donnelly, L. Freidel, S. F. Moosavian, and A. J. Speranza, “Matrix Quantization of Gravitational Edge Modes,” JHEP 05 (2027) 163, arXiv:2212.09120 [hep-th]

    work page arXiv 2027

  72. [72]

    Gravitational edge mode in N = 1 Jackiw-Teitelboim supergravity,

    K.-S. Lee, A. Sivakumar, and J. Yoon, “Gravitational edge mode in N = 1 Jackiw-Teitelboim supergravity,” JHEP 08 (2024) 011, arXiv:2403.17182 [hep-th]

    work page arXiv 2024

  73. [73]

    Minimal Areas from Entangled Matrices,

    J. R. Fliss, A. Frenkel, S. A. Hartnoll, and R. M. Soni, “Minimal Areas from Entangled Matrices,” arXiv:2408.05274 [hep-th]

    work page arXiv

  74. [74]

    From Asymptotic Symmetries to the Corner Proposal,

    L. Ciambelli, “From Asymptotic Symmetries to the Corner Proposal,” PoS Modave2022 (2023) 002, arXiv:2212.13644 [hep-th]

    work page arXiv 2023

  75. [75]

    Entanglement entropy of linearized gravitons in a sphere,

    V. Benedetti and H. Casini, “Entanglement entropy of linearized gravitons in a sphere,” Phys. Rev. D 101 no. 4, (2020) 045004, arXiv:1908.01800 [hep-th]

    work page arXiv 2020

  76. [76]

    Entanglement entropy of gravitational edge modes,

    J. R. David and J. Mukherjee, “Entanglement entropy of gravitational edge modes,” JHEP 08 (2022) 065, arXiv:2201.06043 [hep-th]

    work page arXiv 2022

  77. [77]

    The entropy of finite gravitating regions,

    V. Balasubramanian and C. Cummings, “The entropy of finite gravitating regions,” arXiv:2312.08434 [hep-th]

    work page arXiv

  78. [78]

    Gravitons on the edge,

    A. Blommaert and S. Colin-Ellerin, “Gravitons on the edge,” arXiv:2405.12276 [hep-th] . 63

    work page arXiv

  79. [79]

    Spectra of laplace-beltrami operators on SO( n + 2)/SO(2) × SO(n) and Sp(n + 1)/Sp(1) × Sp(n),

    C. Tsukamoto, “Spectra of laplace-beltrami operators on SO( n + 2)/SO(2) × SO(n) and Sp(n + 1)/Sp(1) × Sp(n),” Osaka Journal of Mathematics 18 no. 2, (1981) 407–426. https://hdl.handle.net/11094/8349. Publisher: Osaka University and Osaka City University, Departments of Mathematics

    work page 1981

  80. [80]

    Topological entanglement entropy

    A. Kitaev and J. Preskill, “Topological entanglement entropy,” Phys. Rev. Lett. 96 (2006) 110404, arXiv:hep-th/0510092

    work page internal anchor Pith review Pith/arXiv arXiv 2006

Showing first 80 references.