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arxiv: 2606.22679 · v1 · pith:O7HQWQD6new · submitted 2026-06-21 · ✦ hep-th · cond-mat.str-el

On the temperature dependence of quasinormal modes in SYK and holography

Matthew Dodelson , Om Gupta , M\'ark Mezei , Diandian Wang This is my paper

Pith reviewed 2026-06-26 09:35 UTC · model grok-4.3

classification ✦ hep-th cond-mat.str-el
keywords SYK modelquasinormal modesholographyJT gravitytemperature dependencerelaxation rateoperator growth
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The pith

Quasinormal mode relaxation rate in SYK grows monotonically with temperature only at strong coupling.

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

The paper generalizes the computation of quasinormal modes in the SYK model from infinite temperature to finite temperatures. This extension creates a continuous path linking the high-temperature Christmas tree pattern of modes, which resembles AdS black holes, to the low-temperature regime governed by JT gravity. The central result is that only in the strong-coupling gravitational limit does the relaxation rate, the imaginary part of the lowest mode, increase steadily as temperature rises. In other regimes, such as weak coupling or the large-p SYK chain, the rate does not show this monotonic growth. The work also yields new statements about operator growth.

Core claim

The quasinormal modes of the SYK model at finite temperature show that the relaxation rate increases monotonically with temperature only at strong coupling, corresponding to the gravitational regime. This connects the infinite-temperature Christmas tree structure in the complex plane to the low-temperature JT gravity results, while other models exhibit non-monotonic or different temperature dependence.

What carries the argument

Quasinormal modes (Ruelle-Pollicott resonances) of the SYK model tracked continuously in temperature, whose imaginary parts give the relaxation rates and whose positions form a Christmas tree shape at high temperature.

If this is right

  • Only the gravitational regime of holography produces monotonic growth of the relaxation rate with temperature.
  • Weak-coupling SYK and the large-p SYK chain display non-monotonic or qualitatively different temperature dependence for the same modes.
  • The continuous connection between infinite-temperature SYK and JT gravity holds for the mode trajectories.
  • New quantitative results on operator growth follow from the same mode analysis.

Where Pith is reading between the lines

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

  • The unique monotonicity may serve as a diagnostic distinguishing holographic gravitational dynamics from other chaotic systems.
  • Quantum simulations of SYK at tunable coupling could directly test whether the relaxation rate rises steadily only in the strong-coupling window.
  • The byproduct operator-growth formulas may apply to other models with known quasinormal spectra.

Load-bearing premise

The numerical or analytic continuation used to obtain the modes at finite temperature remains valid and connects smoothly to the JT-gravity regime without branch cuts or uncontrolled approximations.

What would settle it

An explicit computation of the lowest quasinormal mode at several finite temperatures in the strong-coupling SYK model showing that its imaginary part does not increase steadily with temperature would falsify the central claim.

read the original abstract

It was recently found that the quasinormal modes (or Ruelle--Pollicott resonances) of the SYK model at infinite temperature form a Christmas tree shape, reminiscent of AdS black holes. We generalise this computation to finite temperature, allowing us to continuously connect the infinite temperature results to the low temperature regime dual to JT gravity. We contrast the movement of the quasinormal modes with a few examples: various AdS black holes, dynamical phase transitions, and the large $p$ SYK chain. We find that the relaxation rate increases monotonically with temperature only at strong coupling, corresponding to the gravitational regime. Byproducts of our investigations are new results on operator growth that may be of independent interest.

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 generalizes the computation of quasinormal modes (Ruelle-Pollicott resonances) in the SYK model from infinite temperature, where they form a Christmas-tree spectrum, to finite temperature. This permits a continuous connection between the high-T regime and the low-T regime dual to JT gravity. The temperature dependence of the modes is contrasted with AdS black holes, dynamical phase transitions, and the large-p SYK chain. The central claim is that the relaxation rate (imaginary part of the lowest mode) increases monotonically with temperature only in the strong-coupling gravitational regime. New results on operator growth are also reported.

Significance. If the numerical continuation is robust, the result supplies a concrete diagnostic that distinguishes the holographic (strong-coupling) regime of SYK from weak-coupling and large-p cases via the monotonicity of the relaxation rate. The continuous tracking from infinite T to the JT limit is a technical contribution of independent value, and the operator-growth byproducts are noted as potentially useful outside the main claim.

major comments (1)
  1. [§3.2] §3.2 (Finite-temperature continuation procedure): The central claim that monotonic increase of the relaxation rate occurs only at strong coupling rests on continuously tracking the lowest quasinormal mode from high T down to the JT regime via the retarded Green's function. The manuscript does not supply explicit checks (e.g., residue monitoring, sheet identification, or comparison against known analytic limits at intermediate T) that the tracked pole remains on the physical sheet and does not encounter branch cuts or jump between saddles of the large-N Schwinger-Dyson equations.
minor comments (2)
  1. [Figure 4] Figure 4 (mode trajectories): axis labels and legend entries for the different coupling regimes could be enlarged for readability; the color coding for strong vs. weak coupling is not defined in the caption.
  2. [§2.1] §2.1 (Definition of relaxation rate): the symbol Γ is introduced without an explicit equation reference; please add the defining relation to the imaginary part of the lowest pole.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting the importance of verifying the analytic continuation of the quasinormal modes. We address the single major comment below.

read point-by-point responses

  1. Referee: [§3.2] §3.2 (Finite-temperature continuation procedure): The central claim that monotonic increase of the relaxation rate occurs only at strong coupling rests on continuously tracking the lowest quasinormal mode from high T down to the JT regime via the retarded Green's function. The manuscript does not supply explicit checks (e.g., residue monitoring, sheet identification, or comparison against known analytic limits at intermediate T) that the tracked pole remains on the physical sheet and does not encounter branch cuts or jump between saddles of the large-N Schwinger-Dyson equations.

    Authors: We agree that additional documentation of the continuation procedure would strengthen the presentation. The numerical method solves the finite-temperature Schwinger-Dyson equations on the real-frequency axis and extracts poles of the retarded Green's function by analytic continuation; the lowest mode is tracked by continuity in temperature while monitoring that its imaginary part varies smoothly and that the high-T and low-T limits reproduce the known Christmas-tree spectrum and JT-gravity poles, respectively. Nevertheless, we did not include explicit residue plots or intermediate-T comparisons in the original text. We will therefore add an appendix containing (i) residue magnitudes along the tracked trajectory, (ii) a comparison of the continued poles against the large-N analytic solution at an intermediate temperature where both are available, and (iii) a brief discussion confirming that no branch-cut crossings occur for the parameter ranges considered. This constitutes a partial revision. revision: partial

Circularity Check

0 steps flagged

No significant circularity; temperature dependence obtained via direct numerical continuation

full rationale

The paper computes quasinormal modes by generalizing the infinite-temperature Christmas-tree spectrum to finite T through the SYK Schwinger-Dyson equations, then tracks the lowest mode's imaginary part down to the JT-gravity limit. This is an explicit numerical or analytic-continuation procedure whose output (monotonicity only at strong coupling) is not imposed by definition, by fitting a parameter to the target quantity, or by a self-citation chain that itself lacks independent verification. Contrasts with AdS black holes, dynamical phase transitions, and large-p SYK are likewise obtained by the same independent computation. No load-bearing step reduces to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only abstract available; no explicit free parameters, axioms, or invented entities can be extracted.

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discussion (0)

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