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arxiv: 2606.17167 · v1 · pith:OHP2WP57new · submitted 2026-06-15 · ✦ hep-th · cond-mat.stat-mech· math-ph· math.MP

Thermal One-point Functions and Asymptotic CFT Data: QFT in AdS

Ilija Buri\'c , Francesco Mangialardi , Francesco Russo , Volker Schomerus , Alessandro Vichi This is my paper

Pith reviewed 2026-06-27 02:40 UTC · model grok-4.3

classification ✦ hep-th cond-mat.stat-mechmath-phmath.MP
keywords thermal one-point functionsasymptotic CFT dataAdS/CFTheavy operatorsperturbative bulk interactionsconformal weightsspectral densityOPE coefficients
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The pith

Thermal inversion formulas remain accurate for CFT data at intermediate conformal weights even after including bulk interactions.

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

This paper studies the thermal partition function and one-point functions in a three-dimensional conformal field theory that is dual to a massive interacting scalar field in four-dimensional anti-de Sitter space. Using thermal inversion formulas, the authors extract the asymptotic behavior of the spectral density and operator product expansion coefficients for heavy operators with fixed spin. They first consider the non-interacting case corresponding to a generalized free field, and then include first-order corrections from cubic and quartic interactions in the bulk. The key result is that these asymptotic expressions describe the actual CFT data well even at moderate values of the conformal weight, and that this accuracy is not spoiled by the bulk interactions.

Core claim

The asymptotic formulas obtained from thermal inversion remain quantitatively accurate far from the asymptotic regime, describing CFT data reliably already at intermediate conformal weights. This feature survives the inclusion of bulk interactions from cubic and quartic terms and provides new analytic control over heavy-state data in conformal field theories.

What carries the argument

Thermal inversion formulas applied to thermal one-point functions, which extract asymptotic spectral densities and OPE coefficients for heavy operators at fixed spin in the presence of bulk interactions.

If this is right

  • The asymptotic behaviour of spectral density and OPE coefficients is determined for the generalised free field.
  • First-order perturbative corrections from cubic and quartic bulk interactions are computed.
  • The formulas provide analytic control over a regime dominated by states with large particle number in the bulk.
  • The accuracy at intermediate conformal weights persists when interactions are included.

Where Pith is reading between the lines

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

  • If the inversion formulas apply at this order, similar methods might extract data in other perturbative expansions around AdS.
  • The survival of accuracy suggests that thermal observables can probe high-particle-number states without needing the full non-perturbative solution.
  • Direct comparison to CFT data at intermediate weights could test the validity of the perturbative treatment.

Load-bearing premise

The thermal inversion formulas derived for the free theory continue to apply without modification when first-order perturbative corrections from cubic and quartic bulk interactions are included.

What would settle it

A computation of the one-point functions or spectral data at intermediate weights in the interacting theory that shows significant deviation from the perturbative inversion predictions would falsify the quantitative accuracy claim.

read the original abstract

We investigate the thermal partition and one-point functions of the three-dimensional conformal field theory dual to a massive interacting scalar field in AdS$_4$. Using thermal inversion formulas, we determine the asymptotic behaviour of the spectral density and OPE coefficients involving heavy operators at fixed spin. We first analyse these CFT data for the generalised free field, corresponding to the non-interacting bulk theory. Then we compute the first-order perturbative corrections induced by the cubic and quartic bulk interactions. The thermal observables considered here probe a sector associated with operators of large dimension and, in the bulk description, a regime dominated by states with large particle number. This regime remains comparatively unexplored even in generalised free field theory. Remarkably, the asymptotic formulas obtained from thermal inversion remain quantitatively accurate far from the asymptotic regime, describing CFT data reliably already at intermediate conformal weights. Our results show that this feature survives the inclusion of bulk interactions and provide new analytic control over heavy-state data in conformal field theories.

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 studies thermal partition and one-point functions in the 3d CFT dual to an interacting massive scalar in AdS4. It employs thermal inversion formulas to extract the asymptotic spectral density and OPE coefficients of heavy operators at fixed spin, first in the generalized free field (GFF) limit corresponding to the free bulk theory, and then including O(λ) corrections from cubic and quartic bulk interactions. The central result is that the asymptotic formulas remain quantitatively accurate already at intermediate conformal weights, and that this accuracy persists after the inclusion of bulk interactions.

Significance. If the results hold, the work supplies new analytic expressions for heavy-state CFT data in a regime of large particle number that is otherwise difficult to access. The explicit first-order perturbative corrections to thermal observables, together with the demonstration that thermal inversion remains reliable beyond the strict asymptotic limit, constitute a concrete advance in controlling thermal CFT data via AdS methods. The survival of the accuracy under interactions is a non-trivial statement that strengthens the utility of the inversion technique.

major comments (1)
  1. [Section on perturbative corrections (around the application of inversion formulas to interacting thermal observables)] The central claim that the asymptotic formulas remain accurate with interactions rests on the assumption that the thermal inversion procedure derived for the GFF case applies without modification at O(λ). The manuscript computes the bulk corrections to the thermal partition function and one-point functions but does not provide an explicit argument or calculation showing that the inversion kernel, the light-operator contributions, or the analytic continuation receive no additional O(λ) terms. This step is load-bearing for the direct comparison to CFT data at intermediate weights.
minor comments (2)
  1. The abstract asserts 'quantitative accuracy' and 'reliable' description at intermediate weights, yet no error estimates, fit ranges, or explicit numerical comparison values are mentioned; these should be supplied in the main text or a dedicated comparison section.
  2. Notation for the bulk coupling λ and the precise form of the cubic/quartic vertices should be introduced earlier and used consistently when stating the O(λ) corrections.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading, positive assessment of the significance of the work, and constructive major comment. We address the point raised below.

read point-by-point responses

  1. Referee: The central claim that the asymptotic formulas remain accurate with interactions rests on the assumption that the thermal inversion procedure derived for the GFF case applies without modification at O(λ). The manuscript computes the bulk corrections to the thermal partition function and one-point functions but does not provide an explicit argument or calculation showing that the inversion kernel, the light-operator contributions, or the analytic continuation receive no additional O(λ) terms. This step is load-bearing for the direct comparison to CFT data at intermediate weights.

    Authors: The thermal inversion formulas are general CFT results derived from the OPE expansion of the thermal two-point function and its analytic properties on the thermal cylinder; they do not assume a free or generalized-free spectrum. The GFF analysis in the manuscript serves to illustrate the procedure and to obtain the leading asymptotic expressions, but the underlying inversion kernel, the subtraction of light-operator contributions, and the required analytic continuation are unchanged when the theory is perturbed by bulk interactions. The O(λ) corrections enter exclusively through the thermal partition function and one-point functions that are fed into the inversion; these corrected observables already encode the first-order modifications to both heavy and light data. Because the inversion operation is linear, it applies order by order without generating additional O(λ) terms in the kernel itself. We will add a short clarifying paragraph in the revised manuscript (in the section on perturbative corrections) that states this generality explicitly and confirms that no further modification to the inversion procedure is required at this order. revision: yes

Circularity Check

0 steps flagged

No circularity: thermal inversion applied as external tool to independently computed perturbative corrections

full rationale

The derivation computes O(λ) corrections to the thermal partition function and one-point functions directly from cubic/quartic bulk vertices in the AdS description, then feeds the resulting thermal observables into pre-existing thermal inversion formulas to extract asymptotic spectral densities and OPE coefficients. These formulas are invoked as a standard extraction method rather than being redefined or fitted within the paper; the quantitative accuracy claim is tested by direct comparison to CFT data at intermediate weights, which is an independent check. No step reduces the output to a self-definition, a fitted input renamed as prediction, or a load-bearing self-citation chain. The central result therefore retains independent content from the bulk perturbation calculation.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the applicability of thermal inversion formulas to the interacting perturbative theory and on the validity of the AdS/CFT dictionary for thermal observables; no free parameters or new entities are mentioned in the abstract.

axioms (1)
  • domain assumption Standard axioms of conformal field theory together with the AdS/CFT correspondence for a scalar field in AdS4
    The entire setup is framed inside the AdS/CFT dictionary for a 3d CFT dual to QFT in AdS4.

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discussion (0)

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