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arxiv: 2606.04949 · v1 · pith:2UVJOTB5new · submitted 2026-06-03 · ✦ hep-th · gr-qc

Off-shell Thermodynamics and Kinetics of Holographic CFTs Dual to Charged AdS Black Holes

Debabrata Sahu , Chandrasekhar Bhamidipati This is my paper

Pith reviewed 2026-06-28 05:35 UTC · model grok-4.3

classification ✦ hep-th gr-qc
keywords holographic CFToff-shell free energyphase structurefirst-passage timeAdS black holescharged black holesthermodynamicskinetics
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0 comments X

The pith

Holographic CFTs dual to charged AdS black holes have their phase structure and transition kinetics described by off-shell free energy across three ensembles.

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

The paper uses an off-shell free energy to map the thermodynamics and phase diagrams of holographic conformal field theories that are dual to spherically symmetric charged AdS black holes. Three ensembles are considered, with fixed combinations of charge or potential, volume, central charge, and chemical potential. For the first two ensembles, the off-shell free energy supplies the potential for an ensemble-dependent Fokker-Planck equation that governs stochastic transitions between phases. This yields explicit first-passage-time distributions, mean passage times, and their fluctuations as functions of temperature. The resulting phase structure and kinetics are shown to vary with the value of the electric charge and the central charge.

Core claim

An off-shell free energy furnishes both the thermodynamic potentials and the driving potential for a Fokker-Planck description of stochastic phase transitions in holographic CFTs dual to charged AdS black holes. Phase diagrams are obtained for the ensembles with fixed (Q̃, V, C), (Φ̃, V, C), and (Q̃, V, μ). In the first two ensembles the Fokker-Planck equation produces first-passage-time distributions whose mean and variance are computed over a range of temperatures, with explicit dependence on the electric charge Q̃ and central charge C.

What carries the argument

The off-shell free energy, which generates both the equilibrium thermodynamics and the potential landscape for the Fokker-Planck equation that governs stochastic jumps between competing phases.

If this is right

  • Phase diagrams exist for each of the three fixed-quantity ensembles.
  • Mean first-passage times and their fluctuations can be calculated explicitly as functions of temperature.
  • Both the locations of phase boundaries and the transition rates depend on the electric charge and the central charge.
  • The stochastic description applies uniformly to the competing states identified by the off-shell free energy.

Where Pith is reading between the lines

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

  • The same off-shell construction may be applied to other holographic models with different black-hole solutions to obtain comparable kinetic predictions.
  • Temperature dependence of the passage times could be compared with real-time correlation functions in the dual CFT.
  • Variation with central charge offers a window into how large-N or other CFT parameters control transition rates.

Load-bearing premise

The off-shell free energy correctly captures the free-energy landscape of competing states so that the Fokker-Planck equation derived from it accurately models the stochastic transitions in the chosen ensembles.

What would settle it

A direct computation or numerical simulation of the first-passage-time distribution between phases at several temperatures that deviates systematically from the distribution obtained by solving the Fokker-Planck equation whose potential is the off-shell free energy.

read the original abstract

We study the thermodynamics and phase structure of holographic conformal field theories dual to spherically symmetric charged AdS black holes using an off-shell free energy. We consider three ensembles of the dual CFT with fixed: $(\tilde Q,{\cal V},C)$, $(\tilde \Phi,{\cal V},C)$, and $(\tilde Q,{\cal V},\mu)$ and present their corresponding phase diagrams. For the fixed $(\tilde Q,{\cal V},C)$ and $(\tilde \Phi,{\cal V},C)$ ensembles, we study the transitions between competing states using a stochastic description on the various phases given by off-shell free energy. This is described by an ensemble dependent Fokker-Planck equation, allowing us to compute the first-passage-time distribution, including the mean first passage time and its fluctuations over a range of temperatures. We also examine how the phase structure and the associated kinetics depend on the electric charge $\tilde Q$ and the central charge $C$.

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

0 major / 3 minor

Summary. The manuscript studies the thermodynamics and phase structure of holographic CFTs dual to spherically symmetric charged AdS black holes via an off-shell free energy. It considers three ensembles with fixed (Q̃, V, C), (Φ̃, V, C), and (Q̃, V, μ), derives the corresponding phase diagrams, and for the first two ensembles employs an ensemble-dependent Fokker-Planck equation to compute first-passage-time distributions (including means and fluctuations) and their dependence on electric charge Q̃ and central charge C.

Significance. If the off-shell potentials are correctly obtained from the bulk action and the stochastic model is consistently formulated, the work supplies a systematic comparison of ensemble-dependent phase structures together with explicit kinetic quantities (first-passage times) in a holographic setting. This combination of thermodynamics and stochastic dynamics is a natural extension of existing holographic thermodynamics and could be useful for modeling transition rates in strongly coupled systems.

minor comments (3)
  1. [§2] §2: the definition of the off-shell free energy for the (Q̃, V, μ) ensemble is stated without an explicit derivation from the bulk action; a short appendix or paragraph showing the Legendre transform would improve reproducibility.
  2. [Figures 4,5] Figure 4 and 5: the temperature axis labeling is inconsistent between the two panels (one uses T, the other T/T_c); uniform notation would aid comparison of the first-passage-time curves.
  3. [Eq. (27)] The Fokker-Planck diffusion coefficient is introduced in Eq. (27) but its dependence on the central charge C is not shown explicitly; adding a brief remark on this scaling would clarify the C-dependence plots in §5.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their careful reading and positive assessment of our manuscript on off-shell thermodynamics and kinetics of holographic CFTs. The recommendation for minor revision is noted. No specific major comments were provided in the report, so we have no individual points to address at this stage.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The derivation begins from the standard holographic dictionary relating the bulk charged AdS action to the dual CFT free energy, constructs an off-shell potential for each of the three fixed-quantity ensembles, and feeds that potential into an ensemble-dependent Fokker-Planck operator whose drift term is the gradient of the same potential. Both steps are direct applications of existing holographic thermodynamics and stochastic dynamics; neither the phase diagrams nor the first-passage statistics are obtained by fitting parameters to the target observables and then relabeling the fit as a prediction, nor do they rest on a load-bearing self-citation whose own justification is internal to the present work. The central claims therefore remain independent of the outputs they produce.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only abstract available; the main assumption is the validity of the holographic principle and the off-shell free energy method for these systems. No free parameters or invented entities identifiable from abstract.

axioms (1)
  • domain assumption Holographic duality between CFT and AdS gravity
    The entire study is based on the AdS/CFT correspondence, which is a standard assumption in the field but not proven.

pith-pipeline@v0.9.1-grok · 5708 in / 1352 out tokens · 36220 ms · 2026-06-28T05:35:08.365086+00:00 · methodology

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Reference graph

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