Exact holographic thermal spectral functions: OPE, non-perturbative corrections, and black hole singularity

Hewei Frederic Jia; Mukund Rangamani

arxiv: 2604.10803 · v1 · submitted 2026-04-12 · ✦ hep-th · gr-qc

Exact holographic thermal spectral functions: OPE, non-perturbative corrections, and black hole singularity

Hewei Frederic Jia , Mukund Rangamani This is my paper

Pith reviewed 2026-05-10 15:28 UTC · model grok-4.3

classification ✦ hep-th gr-qc

keywords holographic CFTthermal spectral functionOPEblack hole singularityWKB monodromythermofield double correlatornon-perturbative corrections

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The pith

In even-dimensional holographic CFTs the thermal spectral function at finite momentum factorizes into a perturbative OPE-controlled piece and a non-perturbative piece encoding the black hole singularity.

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

The paper shows that for even-dimensional holographic conformal field theories on Minkowski spacetime with scalar operators of integer dimension, the exact thermal spectral function factorizes. The perturbative part is determined by the operator product expansion involving the stress tensor via a near-boundary analysis. The non-perturbative part contains information about the bulk geometry including the black hole horizon and singularity. Using this factorization the authors compute the complete large-momentum transseries expansion of the non-perturbative contribution with exact WKB techniques applied to the bulk wave equation monodromy. This provides a direct connection between boundary CFT observables and the interior features of the dual black hole.

Core claim

For even-dimensional holographic CFTs on Minkowski spacetime and for scalar primaries with integer dimensions, the exact spectral function at finite momentum factorizes into a perturbative/OPE piece controlled by stress tensor exchange and fixed by a near-boundary analysis, and a non-perturbative piece that encodes information about the bulk interior including the black hole horizon and singularity. The full transseries expansion of the non-perturbative piece at large timelike momentum is obtained by employing exact WKB techniques to compute the monodromy of the bulk wave equation. The singular loci of a spatially averaged thermofield double correlator in the complex time plane are worked up

What carries the argument

The exact factorization of the thermal spectral function into perturbative and non-perturbative components, with the non-perturbative part determined by the monodromy of the bulk wave equation computed via exact WKB.

Load-bearing premise

The factorization and its consequences hold only for even-dimensional CFTs on Minkowski space with scalar primaries of integer dimension.

What would settle it

A calculation of the thermal spectral function in an even-dimensional holographic model that fails to exhibit the predicted factorization into perturbative and non-perturbative pieces would falsify the central claim.

read the original abstract

We study analytic properties of thermal spectral functions of holographic CFTs, examining both their (a) exact properties at finite momentum and (b) asymptotics at large momentum. For even-dimensional holographic CFTs on Minkowski spacetime and for scalar primaries with integer dimensions, we demonstrate that the exact spectral function at finite momentum factorizes into a perturbative/OPE piece and a non-perturbative piece. The former is controlled by stress tensor exchange and fixed by a near-boundary analysis. The latter encodes information about the bulk interior, including the black hole horizon and singularity. Utilizing the exact factorization, we obtain the full transseries expansion of the non-perturbative piece at large timelike momentum. This is achieved by employing exact WKB techniques to compute the monodromy of the bulk wave equation. Finally, we use these results to work out the singular loci of a spatially averaged thermofield double correlator in the complex time plane. These singular loci have been argued to provide imprints of the black hole curvature singularity in the dual CFT observables. Our result, which includes the case of non-vanishing momentum, gives a clear link between the non-perturbative spectral function and the black hole singularity.

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.

Desk Editor's Note private letter to a colleague

The paper gives an exact factorization of finite-momentum thermal spectral functions into OPE and non-perturbative pieces for even-dimensional holographic CFTs with integer-dimension scalars, then extracts the full large-momentum transseries of the non-perturbative part via exact WKB monodromy and links the resulting singular loci to the black-hole singularity.

read the letter

The main advance is the clean separation at finite momentum: the perturbative piece is fixed entirely by stress-tensor exchange and near-boundary data, while the non-perturbative piece, which carries the bulk interior information, is computed as a complete transseries at large timelike momentum using exact WKB on the bulk wave equation. They then locate the singular loci of the spatially averaged thermofield-double correlator in the complex-time plane and argue these loci encode the black-hole curvature singularity. This is a concrete analytic result rather than another approximation, and the exact WKB monodromy step avoids parameter fitting, which is a clear improvement over typical holographic spectral-function work. The factorization itself is new at non-zero momentum and the transseries plus singularity link is a direct step toward making interior geometry visible in boundary observables. The restrictions are stated plainly—only even dimensions, Minkowski boundary, integer-dimension scalars—so the result does not claim broader validity. Those limits keep the derivation tractable but also narrow its immediate reach. The abstract is internally consistent and the method looks reproducible, but the soundness of the monodromy calculation and the precise mapping from singular loci to curvature singularity would need checking in the full text. No circularity or hidden fitting appears in the stated approach. This is for people already working on exact holographic correlators, thermal spectral functions, or bulk reconstruction questions. A reader focused on non-perturbative AdS/CFT methods will get usable new expressions and a clear technical path. It deserves peer review because the claims are specific, the assumptions are explicit, and the calculations can be verified directly.

Referee Report

0 major / 3 minor

Summary. The manuscript analyzes analytic properties of thermal spectral functions in holographic CFTs. For even-dimensional holographic CFTs on Minkowski spacetime with scalar primaries of integer dimension, it demonstrates that the exact spectral function at finite momentum factorizes into a perturbative/OPE-controlled piece (fixed by near-boundary stress-tensor exchange) and a non-perturbative piece encoding bulk interior information including the black-hole horizon and singularity. Exact WKB techniques are applied to the bulk wave equation to obtain the full transseries expansion of the non-perturbative piece at large timelike momentum; the results are then used to determine the singular loci of the spatially averaged thermofield-double correlator in the complex time plane, establishing a direct link between the non-perturbative spectral function and the black-hole curvature singularity.

Significance. If the central claims hold, the work provides a precise, parameter-free connection between boundary spectral functions and bulk geometry via an exact factorization and monodromy computation. The explicit use of exact WKB to generate the transseries without auxiliary fitting, together with the resulting falsifiable prediction for TFD-correlator singularities, strengthens the holographic dictionary for non-perturbative observables. The restrictions to even boundary dimension, Minkowski space, and integer operator dimension are stated clearly, rendering the result well-scoped and testable within its domain.

minor comments (3)

The introduction would benefit from a brief explicit statement of the precise normalization chosen for the spectral function (e.g., relative to the two-point function convention) to facilitate comparison with existing literature.
Figure captions for the plots of the transseries coefficients should include the numerical values of the first few terms so that readers can immediately verify the claimed asymptotic behavior.
A short remark on the extension (or lack thereof) to odd-dimensional boundary theories would help clarify the scope without altering the main claims.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the positive summary and recommendation of minor revision. The referee's description accurately reflects the scope and results of our analysis on the exact factorization of thermal spectral functions in even-dimensional holographic CFTs and the application of exact WKB to extract transseries expansions linked to bulk singularities.

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper's factorization of the spectral function into perturbative (near-boundary OPE) and non-perturbative pieces is obtained by direct analysis of the bulk wave equation. The non-perturbative transseries at large momentum follows from exact WKB monodromy computation on that equation, and the singular loci of the thermofield-double correlator are read off from the resulting data. No step reduces by the paper's own equations to a fitted parameter, self-definition, or load-bearing self-citation; the assumptions (even dimension, integer scalar dimension, Minkowski boundary) are explicitly scoped and do not smuggle in the target result.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on the standard holographic dictionary relating CFT spectral functions to bulk wave equations in an AdS black hole geometry. No new free parameters or invented entities are introduced. The analysis is restricted to even dimensions and integer-dimensional scalars, which are domain assumptions rather than fitted quantities.

axioms (2)

domain assumption The AdS/CFT correspondence maps thermal spectral functions of the boundary CFT to solutions of the bulk wave equation in a black hole geometry.
Invoked throughout to equate CFT observables with bulk quantities; stated in the abstract's framing of holographic CFTs.
domain assumption The bulk geometry is a classical AdS black hole whose wave equation admits an exact WKB treatment for monodromy.
Required for the non-perturbative expansion and the link to the curvature singularity.

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discussion (0)

Forward citations

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Reference graph

Works this paper leans on

2 extracted references · 2 canonical work pages · cited by 1 Pith paper

[1]

Fooling the Censor: Going beyond inner horizons with the OPE

arXiv:2404.17286 [hep-th]. [ˇCLPV25] Nejc ˇCeplak, Hong Liu, Andrei Parnachev, and Samuel Valach. “Fooling the Censor: Going beyond inner horizons with the OPE”. In: (Nov. 2025). arXiv: 2511.09638 [hep-th]. [DDP97] Eric Delabaere, Herv´ e Dillinger, and Fr´ ed´ eric Pham. “Exact semiclassical ex- pansions for one-dimensional quantum oscillators”. In:J. Ma...

work page doi:10.1063/1.532206 2025
[2]

The Black hole singularity in AdS / CFT

arXiv:1903.05306 [hep-th]. [FHKS04] Lukasz Fidkowski, Veronika Hubeny, Matthew Kleban, and Stephen Shenker. “The Black hole singularity in AdS / CFT”. In:JHEP02 (2004), p. 014.doi: 10.1088/1126-6708/2004/02/014. arXiv:hep-th/0306170. [FL06] Guido Festuccia and Hong Liu. “Excursions beyond the horizon: Black hole singularities in Yang-Mills theories. I.” I...

work page doi:10.1088/1126-6708/2004/02/014 1903

[1] [1]

Fooling the Censor: Going beyond inner horizons with the OPE

arXiv:2404.17286 [hep-th]. [ˇCLPV25] Nejc ˇCeplak, Hong Liu, Andrei Parnachev, and Samuel Valach. “Fooling the Censor: Going beyond inner horizons with the OPE”. In: (Nov. 2025). arXiv: 2511.09638 [hep-th]. [DDP97] Eric Delabaere, Herv´ e Dillinger, and Fr´ ed´ eric Pham. “Exact semiclassical ex- pansions for one-dimensional quantum oscillators”. In:J. Ma...

work page doi:10.1063/1.532206 2025

[2] [2]

The Black hole singularity in AdS / CFT

arXiv:1903.05306 [hep-th]. [FHKS04] Lukasz Fidkowski, Veronika Hubeny, Matthew Kleban, and Stephen Shenker. “The Black hole singularity in AdS / CFT”. In:JHEP02 (2004), p. 014.doi: 10.1088/1126-6708/2004/02/014. arXiv:hep-th/0306170. [FL06] Guido Festuccia and Hong Liu. “Excursions beyond the horizon: Black hole singularities in Yang-Mills theories. I.” I...

work page doi:10.1088/1126-6708/2004/02/014 1903