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arxiv: 2606.26163 · v1 · pith:77QY6QKRnew · submitted 2026-06-24 · ✦ hep-th

Large-N Carrollian Thermodynamics from AdS Black-Hole Phase-Space Contractions

Yingnan Xu , Shuangshuang Chu This is my paper

Pith reviewed 2026-06-26 01:34 UTC · model grok-4.3

classification ✦ hep-th
keywords Carrollian thermodynamicsAdS/CFT correspondenceblack hole phase spacelarge-N ensembleholographic stress tensorsupertranslation chargescelestial correlatorsHawking-Page transition
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The pith

Contracting the AdS time generator and Newton constant produces a finite Carrollian first law with a large-N holographic interpretation.

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

By contracting the phase space of the time generator and Newton constant, the paper shows that the extended AdS first law acquires a finite Carrollian limit. This finite line is given a holographic reading as a double-scaled low-temperature large-N ensemble, with Carrollian temperature falling while boundary degrees of freedom increase to keep products finite. The dictionary is fixed by AdS5/CFT4 and AdS3/CFT2 conventions. The construction leads to a finite boundary stress tensor whose energy matches the bulk Hamiltonian and to a first law phrased in spatial volume and degree-of-freedom count, with the Hawking-Page point marking zero chemical potential for those degrees of freedom.

Core claim

The finite first-law line obtained from the phase-space contraction has a holographic interpretation as a double-scaled low-temperature, large-N ensemble in which the Carrollian temperature decreases while the effective number of boundary degrees of freedom grows, leaving the thermodynamic products finite. This is anchored by AdS5/CFT4 normalization of adjoint degrees of freedom and Brown-Henneaux central charge in AdS3/CFT2. The boundary form of the first law is expressed using spatial volume and the holographic normalization, with the Hawking-Page locus as the zero of the conjugate chemical potential.

What carries the argument

The phase-space contraction of the time generator and Newton constant, which ensures the extended AdS first law has a finite Carrollian limit and allows mapping to a double-scaled boundary ensemble.

If this is right

  • The finite Carrollian Brown-York stress tensor on the contracted AdS boundary has global energy charge equal to the finite bulk Hamiltonian.
  • The boundary first law is written in terms of the spatial volume and the holographic degree-of-freedom normalization.
  • The Hawking-Page locus is identified with the zero of the chemical potential conjugate to the count of degrees of freedom.
  • The finite first law corresponds to the thermal zero-mode sector of the Carrollian Ward identity.
  • The finite celestial-basis correlators are rescaled double-scaled correlators from the Fourier-Mellin transform combined with rescaled thermal frequency window.

Where Pith is reading between the lines

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

  • This double-scaling procedure may extend to other holographic dualities involving Carrollian limits or ultrarelativistic regimes.
  • Connecting to celestial holography suggests new ways to compute thermal correlators in Carrollian CFTs.
  • The identification of supertranslation charges with thermodynamic quantities could link to asymptotic symmetries in flat space limits.

Load-bearing premise

The phase-space contraction of the time generator and Newton constant produces an extended AdS first law that possesses a finite Carrollian limit.

What would settle it

An explicit computation in a specific AdS black hole background showing that after contraction the first law diverges or fails to match the proposed large-N boundary counting would falsify the claim.

Figures

Figures reproduced from arXiv: 2606.26163 by Shuangshuang Chu, Yingnan Xu.

Figure 1
Figure 1. Figure 1: FIG. 1: Structure of the holographic Carrollian [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Finite Carrollian Hawking–Page diagram for [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
read the original abstract

We develop the boundary and celestial interpretation of finite Carrollian black-hole thermodynamics. The bulk input is the phase-space contraction of the time generator and Newton constant for which the extended AdS first law has a finite Carrollian limit. We show that this finite first-law line has a holographic interpretation as a double-scaled low-temperature, large-$N$ ensemble: the Carrollian temperature decreases while the effective number of boundary degrees of freedom grows, leaving the thermodynamic products in the first law finite. The large-$N$ dictionary is anchored by the standard $\mathrm{AdS}_5/\mathrm{CFT}_4$ normalization of adjoint degrees of freedom and by the Brown--Henneaux central charge in $\mathrm{AdS}_3/\mathrm{CFT}_2$. We construct the finite Carrollian Brown--York stress tensor on the contracted AdS boundary and show that its global energy charge is the finite bulk Hamiltonian. We then derive the boundary form of the first law in terms of the spatial volume and the holographic degree-of-freedom normalization. This identifies the Hawking--Page locus with the zero of the chemical potential conjugate to the count of degrees of freedom. The same charge is the global Carrollian supertranslation charge, so the finite first law is the thermal zero-mode sector of the Carrollian Ward identity. Finally, we construct the celestial conformal-primary representation of thermal Carrollian correlators. The finite celestial-basis correlators are rescaled double-scaled correlators obtained by combining the Fourier--Mellin transform with the rescaled thermal frequency window.

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

1 major / 2 minor

Summary. The paper claims that a phase-space contraction of the time generator and Newton constant in AdS black holes produces a finite Carrollian limit of the extended first law. This finite first-law line is interpreted holographically as a double-scaled low-temperature, large-N ensemble in which Carrollian temperature decreases while the effective number of boundary degrees of freedom grows so that thermodynamic products remain finite. The large-N dictionary is fixed by standard AdS5/CFT4 adjoint dof counting and the Brown-Henneaux central charge. The work constructs the finite Carrollian Brown-York stress tensor (whose global energy equals the finite bulk Hamiltonian), derives the boundary first law in terms of spatial volume and dof normalization, identifies the Hawking-Page locus with vanishing chemical potential conjugate to dof count, shows that the same charge is the global Carrollian supertranslation charge (hence the first law is the thermal zero-mode sector of the Carrollian Ward identity), and constructs celestial conformal-primary representations of thermal Carrollian correlators via a Fourier-Mellin transform combined with a rescaled thermal frequency window.

Significance. If the contraction is shown to preserve the first-law identity without residual terms, the construction supplies a controlled route from AdS black-hole thermodynamics to finite Carrollian boundary structures, with explicit stress-tensor and celestial-correlator realizations that could be useful for flat-space holography and Carrollian CFT studies. The anchoring to standard AdS/CFT normalizations is a concrete strength.

major comments (1)
  1. [section deriving the finite Carrollian first law (phase-space contraction)] The central claim that the chosen contraction of the time generator and Newton constant yields a finite Carrollian first law rests on the assumption that the limit commutes with the exterior derivative δ. The manuscript must explicitly verify that no residual terms from the original AdS asymptotics appear after the contraction (i.e., that the thermodynamic identity is preserved without extra assumptions on the black-hole parameters). This verification is load-bearing for the finite-limit and holographic-ensemble statements.
minor comments (2)
  1. [introduction of contraction parameters] Notation for the contracted time generator and the rescaled Newton constant should be introduced with an explicit equation at first appearance to avoid ambiguity when the limit is taken.
  2. [abstract and §2] The abstract states the constructions but supplies no sample derivations or checks; a brief illustrative calculation (e.g., for the Schwarzschild-AdS case) in the main text would improve readability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address the single major comment below.

read point-by-point responses

  1. Referee: [section deriving the finite Carrollian first law (phase-space contraction)] The central claim that the chosen contraction of the time generator and Newton constant yields a finite Carrollian first law rests on the assumption that the limit commutes with the exterior derivative δ. The manuscript must explicitly verify that no residual terms from the original AdS asymptotics appear after the contraction (i.e., that the thermodynamic identity is preserved without extra assumptions on the black-hole parameters). This verification is load-bearing for the finite-limit and holographic-ensemble statements.

    Authors: We agree that an explicit verification of the commutation between the phase-space contraction and the exterior derivative δ is required to confirm the absence of residual terms. In the revised manuscript we have inserted a new paragraph immediately following the definition of the contracted generators. There we first apply the scaling to the extended first-law identity (before δ acts), then take the simultaneous limit on each term separately. Because the contraction is linear in the generators and the Newton constant, and because the AdS asymptotic contributions that could produce non-vanishing residuals are multiplied by positive powers of the contraction parameter that are sent to zero, no extra terms survive. The calculation uses only the same black-hole parameter scalings already stated for the finite limit to exist; no additional assumptions are introduced. This step-by-step verification is now part of the main text and directly supports the subsequent holographic-ensemble statements. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation anchored by external AdS/CFT benchmarks

full rationale

The paper selects a phase-space contraction of the time generator and Newton constant as the bulk input chosen specifically so that the extended AdS first law admits a finite Carrollian limit. The subsequent claim that this finite line corresponds to a double-scaled low-temperature large-N ensemble is then anchored by the standard AdS5/CFT4 normalization of adjoint degrees of freedom and the Brown-Henneaux central charge, both of which are independent external references rather than self-derived quantities. No quoted step reduces a prediction or first-principles result to a fitted parameter, self-citation chain, or definitional renaming; the thermodynamic products remain finite by the explicit scaling choice, but the holographic dictionary itself does not collapse to that choice. The derivation is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract does not specify any free parameters, axioms, or invented entities; the phase-space contraction and large-N scaling may involve implicit assumptions but no details are given.

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