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arxiv: 2502.13208 · v2 · pith:QMT7DLKDnew · submitted 2025-02-18 · ✦ hep-th · gr-qc· math-ph· math.MP· quant-ph

Finite cutoff JT gravity: Baby universes, Matrix dual, and (Krylov) Complexity

Arpan Bhattacharyya , Saptaswa Ghosh , Sounak Pal , Anandu Vinod This is my paper

Pith reviewed 2026-05-23 02:23 UTC · model grok-4.3

classification ✦ hep-th gr-qcmath-phmath.MPquant-ph
keywords finite cutoff JT gravityEinstein-Rosen bridgebaby universesmatrix model dualKrylov complexitycomplexity-volume proposalspectral deformationmoduli space volume
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0 comments X

The pith

Finite cutoff deforms JT gravity so the Einstein-Rosen bridge saturates faster than in the pure theory.

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

The paper applies the complexity=volume conjecture to JT gravity with a finite radial cutoff, which introduces an integrable irrelevant deformation. This deformation changes the spectrum of the dual matrix model and causes the late-time growth of the black-hole interior to saturate sooner than in the undeformed case. The same deformation modifies the emission rate of baby universes once Lorentzian time evolution is turned on, and the relative saturation time depends on the inverse temperature. The work also examines how the cutoff alters the dual matrix model, including possible one-cut universality and non-perturbative shifts in the volume of the moduli space.

Core claim

In finite-cutoff JT gravity the length of the Einstein-Rosen bridge saturates at late times more rapidly than in pure JT gravity because the integrable irrelevant deformation modifies the spectral properties non-trivially; the saturation time relative to the undeformed theory depends on the inverse temperature, the probability of baby-universe emission changes only when Lorentzian evolution is activated, and the dual matrix model exhibits one-cut universality together with non-perturbative corrections to the moduli-space volume induced by the deformed spectral curve.

What carries the argument

The integrable irrelevant deformation generated by the finite radial cutoff, which alters the spectral curve of the matrix-model dual and thereby controls late-time volume growth.

If this is right

  • The deformation parameter controls how quickly the interior volume stops growing.
  • Baby-universe emission rates receive a deformation correction only under Lorentzian evolution.
  • The relative saturation time between deformed and undeformed theories varies with temperature.
  • Non-perturbative corrections appear in the volume of the moduli space through changes to the spectral curve.

Where Pith is reading between the lines

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

  • The temperature dependence of saturation time may produce distinct late-time signatures in thermal ensembles of the deformed theory.
  • If Krylov complexity tracks ERB length in the deformed model, the same faster saturation should appear in operator growth measures.
  • The one-cut universality noted in the matrix dual could simplify calculations of other observables once the cutoff is fixed.

Load-bearing premise

The complexity-equals-volume proposal continues to hold without modification inside the finite-cutoff deformed theory.

What would settle it

An explicit calculation of the late-time ERB length in the finite-cutoff model that shows the same saturation time as pure JT gravity would falsify the central claim.

read the original abstract

In this paper, as an application of the `Complexity = Volume' proposal, we calculate the growth of the interior of a black hole at late times for finite cutoff JT gravity. Due to this integrable, irrelevant deformation, the spectral properties are modified non-trivially. The Einstein-Rosen Bridge (ERB) length saturates faster than pure JT gravity. We comment on the possible connection between Krylov Complexity and ERB length for the deformed theory. Apart from this, we compute the emission probability of baby universes in the deformed theory and find that it changes due to the deformation parameter only if we turn on Lorentzian evolution. We also find that the saturation time of the deformed theory relative to the undeformed one depends on the inverse temperature. We also highlight the subtleties involved in the dual matrix model and comment on the possible one-cut universality. Finally, we comment on the possible correction to the volume of the moduli space arising from the non-perturbative correction of the spectral curve induced by the finite boundary cutoff.

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 manuscript applies the Complexity=Volume proposal to finite-cutoff JT gravity deformed by an integrable irrelevant operator. It claims that the ERB length saturates faster than in pure JT gravity due to modified spectral properties, computes baby-universe emission probabilities that depend on the deformation parameter only under Lorentzian evolution, discusses subtleties in the dual matrix model and possible one-cut universality, comments on a possible link between Krylov complexity and ERB length, and notes potential non-perturbative corrections to the moduli-space volume arising from the deformed spectral curve.

Significance. If the central assumption holds, the work supplies a concrete illustration of how an irrelevant deformation alters late-time interior growth and complexity measures in a solvable 2d gravity model. The reported inverse-temperature dependence of the relative saturation time and the matrix-model analysis could inform studies of deformed JT gravity and its holographic duals.

major comments (1)
  1. [ERB length calculation and Complexity=Volume application] The headline claim that the ERB length saturates faster is obtained by applying the standard, unmodified Complexity=Volume dictionary directly to the deformed geometry and spectral curve. The manuscript does not derive a corrected dictionary or demonstrate that the volume operator remains invariant under the irrelevant deformation, which is load-bearing for linking the deformation parameter to the observed saturation time.
minor comments (2)
  1. [Abstract] The abstract states that saturation time depends on inverse temperature but does not give the functional form; including the explicit dependence in the main text would improve clarity.
  2. [Baby universe emission section] The discussion of baby-universe emission probabilities would benefit from an explicit formula showing how the deformation parameter enters only in the Lorentzian case.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback. We respond to the single major comment below.

read point-by-point responses

  1. Referee: The headline claim that the ERB length saturates faster is obtained by applying the standard, unmodified Complexity=Volume dictionary directly to the deformed geometry and spectral curve. The manuscript does not derive a corrected dictionary or demonstrate that the volume operator remains invariant under the irrelevant deformation, which is load-bearing for linking the deformation parameter to the observed saturation time.

    Authors: We agree that the manuscript applies the standard Complexity=Volume proposal without deriving a modified dictionary from the deformed boundary theory. The ERB length is obtained by evaluating the volume of the maximal slice using the geometry whose properties are determined by the deformed spectral curve; the deformation enters through this modified geometry rather than through an altered dictionary. Because the volume is a purely geometric quantity, we take the standard dictionary to remain applicable at leading order for this integrable deformation. We have added a short clarifying paragraph in the introduction (new paragraph after Eq. (2.3)) stating the assumption explicitly and noting that a first-principles derivation of the dictionary under the irrelevant operator lies outside the present scope. revision: partial

Circularity Check

0 steps flagged

No significant circularity; C=V applied as external proposal

full rationale

The derivation applies the Complexity=Volume proposal (an external assumption) to compute ERB length in the finite-cutoff deformed JT gravity, where the deformation modifies the spectral curve and late-time properties. Saturation times and baby-universe emission probabilities are computed from the deformed geometry under this dictionary; no equation defines the output in terms of itself, no fitted parameter is relabeled as a prediction, and no self-citation chain is invoked to justify the central dictionary. The result is a direct calculation under stated assumptions rather than a reduction to inputs by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Abstract-only review yields an incomplete ledger; the central claims rest on the complexity=volume proposal and standard JT-gravity assumptions whose details are not visible.

free parameters (1)
  • deformation parameter
    Finite cutoff introduces a parameter that modifies spectral properties and saturation times.
axioms (1)
  • domain assumption Complexity equals volume proposal
    Invoked to equate interior growth with ERB length.

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discussion (0)

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Forward citations

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