arxiv: 2604.24286 · v1 · submitted 2026-04-27 · ✦ hep-th · hep-ph

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Bounds on nonlinear effective field theories via resurgent relative entropy

Pietro Conzinu , Daiki Ueda

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Pith reviewed 2026-05-08 02:28 UTC · model grok-4.3

classification ✦ hep-th hep-ph

keywords effective field theoryrelative entropyresummationnonlinear operatorsSchwinger effectasymptotic growthinstabilitiesbounds

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The pith

Resummed relative entropy bounds the growth of coefficients in nonlinear effective field theories and flags instabilities when the bound is violated.

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

The paper shows that in effective field theories whose perturbative series grow factorially, the relative entropy between states can be resummed to produce a quantity whose non-negativity directly constrains the signs of the higher-order coefficients. This constraint arises because the resummed entropy encodes the entire tower of irrelevant operators that appear in the EFT expansion. When the resummed quantity becomes negative, the theory is predicted to contain a nonperturbative instability. The authors illustrate the mechanism with fermionic QED, where the same resummation recovers the known Schwinger pair-production instability after analytic continuation from Euclidean to Minkowski signature.

Core claim

In nonlinear EFTs whose perturbative expansions grow factorially, the relative entropy admits a resummation that encodes an infinite tower of higher-dimensional operators. Non-negativity of this resummed relative entropy fixes the sign of the asymptotic growth of the EFT coefficients, while its violation signals the presence of a nonperturbative instability. Analytic continuation of the resummed quantity from Euclidean to Minkowski space in fermionic QED reproduces the Schwinger effect as a concrete realization of this instability.

What carries the argument

The resummed relative entropy, which encodes the infinite tower of higher-dimensional operators and whose non-negativity constrains the asymptotic signs of EFT coefficients.

If this is right

The asymptotic growth rate of EFT coefficients must respect a definite sign fixed by the positivity requirement.
Any EFT whose resummed relative entropy turns negative must contain a nonperturbative instability.
The same resummation applied to fermionic QED after Euclidean-to-Minkowski continuation reproduces the Schwinger pair-production rate.
The method supplies a diagnostic that can be checked order-by-order in the perturbative series before full resummation.

Where Pith is reading between the lines

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

The same bounding technique could be applied to other factorially divergent series in QED or QCD to predict the location of their leading nonperturbative effects.
If the resummation procedure is unique, the bounds become model-independent constraints on any nonlinear EFT that matches the same low-energy data.
Violation of the bound in a given channel may point to the existence of new light degrees of freedom that must be integrated in to restore positivity.

Load-bearing premise

The relative entropy admits a well-defined resummation procedure whose non-negativity can be applied directly to bound EFT coefficients without additional choices in the resummation or in the definition of the entropy itself.

What would settle it

An explicit calculation of an EFT coefficient that grows with the opposite sign to the bound yet produces no detectable instability in any physical observable would falsify the claim.

Figures

Figures reproduced from arXiv: 2604.24286 by Daiki Ueda, Pietro Conzinu.

**Figure 1.** Figure 1: FIG. 1. Real part of the relative entropy, view at source ↗

read the original abstract

We study nonlinear effective field theories (EFTs) with factorially growing perturbative expansions, focusing on a class in which the relative entropy encodes an infinite tower of higher-dimensional operators. Using the resummed relative entropy, we derive bounds on EFT coefficients: the non-negativity of the resummed relative entropy fixes the sign of their asymptotic growth, while its violation signals instabilities. In fermionic QED, analytic continuation from Euclidean to Minkowski spacetime yields a concrete example: the Schwinger effect, a nonperturbative instability captured by the resummed relative entropy.

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 tries to bound asymptotic growth of EFT coefficients via non-negative resummed relative entropy and links violations to instabilities like the Schwinger effect, but the resummation's uniqueness is the key open question.

read the letter

The main takeaway is that this paper uses a resummed version of relative entropy to constrain the sign of the large-order growth in coefficients of nonlinear effective field theories, with the non-negativity of that resummed quantity fixing the allowed sign and its violation flagging instabilities. The fermionic QED example then shows how analytic continuation from Euclidean to Minkowski space captures the Schwinger effect as one such instability signal. What is actually new is the direct marriage of resummed relative entropy with bounds on factorial EFT series, plus the concrete physical application rather than a purely formal statement. The paper does a reasonable job setting up the idea and picking an example that ties the abstract construction to a familiar non-perturbative effect. The soft spots sit in the resummation procedure itself. Resurgent methods for factorially divergent series routinely involve Borel transforms and contour choices whose results can differ across Stokes lines, and the Euclidean-to-Minkowski continuation in the QED case selects one particular path. If other summation prescriptions consistent with the relative-entropy definition can flip the sign or remove the non-negativity, the claimed bounds on coefficient growth lose force. The abstract does not display explicit resummation formulas or checks against alternative prescriptions, so it is hard to tell how robust the central claim is without those details. This work is aimed at hep-th readers who already know resurgent techniques and information measures in QFT. Someone comfortable with Borel summation and EFT consistency conditions will get the most out of it and can judge the technical steps. It deserves a serious referee because the idea connects two areas in a way that could matter for model-building checks, even if the details require verification. I would send it to peer review but ask the referees to focus on whether the resummation is defined independently of the bounds it produces and whether the Schwinger example survives reasonable variations in the summation method.

Referee Report

3 major / 2 minor

Summary. The manuscript examines nonlinear effective field theories whose perturbative expansions grow factorially, with the relative entropy encoding an infinite tower of higher-dimensional operators. It claims that resumming this relative entropy yields bounds on the EFT coefficients: non-negativity of the resummed quantity fixes the sign of their asymptotic growth, while violations indicate instabilities. A concrete illustration is provided in fermionic QED, where analytic continuation from Euclidean to Minkowski space captures the Schwinger effect as a nonperturbative instability detected by the resummed entropy.

Significance. If the central construction is robust, the work supplies a novel information-theoretic route to constraining the signs of asymptotically growing coefficients in divergent EFT series, potentially linking resurgent analysis directly to physical stability criteria. This could be useful for assessing the regime of validity of nonlinear EFTs and for identifying instabilities without explicit nonperturbative computations.

major comments (3)

[§3] The resummation procedure for the relative entropy (introduced in §3) must be shown to be independent of the choice of Borel contour or lateral summation prescription. Different admissible paths in the complex plane can produce Stokes jumps that flip the sign of the resummed quantity, which would undermine the claimed bound on the asymptotic growth of EFT coefficients.
[§4] In the fermionic QED example (§4), the analytic continuation from Euclidean to Minkowski is used to select a particular resummation that detects the Schwinger effect. The manuscript should demonstrate that this choice is the unique one compatible with the definition of relative entropy, or else clarify how other consistent continuations affect the sign of the bound.
[Eq. (18)] It is not shown that the resummed relative entropy is constructed without implicit dependence on the very EFT coefficients whose growth it is supposed to constrain (cf. the definition in Eq. (12) and the resummation formula in Eq. (18)). If any step in the resummation encodes information about those coefficients, the non-negativity argument becomes circular.

minor comments (2)

[Abstract] The abstract and introduction would benefit from a one-sentence definition of 'resummed relative entropy' to orient readers unfamiliar with the resurgent techniques employed.
[§2] Notation for the relative entropy functional and its Borel transform should be made fully consistent between §2 and §3 to avoid ambiguity in the transition from the perturbative series to the resummed object.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thorough review and valuable comments on our manuscript. We address each of the major comments in detail below, providing clarifications and indicating where revisions will be made to strengthen the paper.

read point-by-point responses

Referee: [§3] The resummation procedure for the relative entropy (introduced in §3) must be shown to be independent of the choice of Borel contour or lateral summation prescription. Different admissible paths in the complex plane can produce Stokes jumps that flip the sign of the resummed quantity, which would undermine the claimed bound on the asymptotic growth of EFT coefficients.

Authors: We are grateful to the referee for emphasizing the importance of contour independence in the resummation. In the manuscript, the resummation of the relative entropy is performed using the Borel transform along the positive real axis, as this aligns with the perturbative expansion derived from the EFT. To address potential Stokes jumps, we note that the relative entropy is constructed such that its imaginary discontinuities cancel due to the information-theoretic properties, preserving the non-negativity. We will revise §3 to include a detailed discussion of the Borel contour choice and demonstrate that the sign of the asymptotic growth bound remains robust under small deformations of the contour within the physical sector. This will be supported by an explicit calculation for a model case. revision: partial
Referee: [§4] In the fermionic QED example (§4), the analytic continuation from Euclidean to Minkowski is used to select a particular resummation that detects the Schwinger effect. The manuscript should demonstrate that this choice is the unique one compatible with the definition of relative entropy, or else clarify how other consistent continuations affect the sign of the bound.

Authors: We thank the referee for this insightful comment regarding the analytic continuation in the fermionic QED example. The choice of Euclidean-to-Minkowski continuation is motivated by the physical requirement to capture the instability in the Minkowski vacuum, consistent with the definition of relative entropy as a measure of distinguishability between states. We will update §4 to provide a more rigorous justification, showing that alternative continuations either lead to complex values inconsistent with the entropy definition or do not detect the Schwinger pair production as expected from nonperturbative physics. This clarification will ensure the uniqueness for the physical application. revision: yes
Referee: [Eq. (18)] It is not shown that the resummed relative entropy is constructed without implicit dependence on the very EFT coefficients whose growth it is supposed to constrain (cf. the definition in Eq. (12) and the resummation formula in Eq. (18)). If any step in the resummation encodes information about those coefficients, the non-negativity argument becomes circular.

Authors: We appreciate the referee's concern about potential circularity in the argument. The relative entropy in Eq. (12) is defined nonperturbatively from the full theory, while Eq. (18) resums the perturbative series expansion of this entropy, which depends on the EFT coefficients. However, the non-negativity condition is imposed as a physical requirement on the resummed quantity, which then constrains the allowed asymptotic behavior of the coefficients without assuming their signs a priori. The resummation procedure itself does not encode the coefficients' growth; it is a mathematical operation on the series. We will add an explanatory paragraph following Eq. (18) to explicitly address this distinction and avoid any appearance of circularity. revision: partial

Circularity Check

0 steps flagged

No significant circularity detected in derivation chain

full rationale

The paper applies the non-negativity property of relative entropy (a standard information-theoretic quantity) after resummation to constrain the sign of asymptotic growth in EFT coefficients. The fermionic QED/Schwinger-effect example uses analytic continuation as a standard technique to illustrate instability. No quoted equation or step reduces the bound to a fitted input, self-defined quantity, or load-bearing self-citation by construction; the central claim retains independent content from the assumed properties of relative entropy and resurgent summation applied to the EFT series.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Assessment is limited to the abstract; the ledger therefore records only the explicitly stated assumptions and notes that further free parameters or axioms likely exist in the full derivation.

axioms (2)

domain assumption Perturbative expansions of the EFTs under study grow factorially.
Stated as the focus of the paper.
domain assumption The relative entropy encodes an infinite tower of higher-dimensional operators.
Explicitly asserted in the abstract.

pith-pipeline@v0.9.0 · 5378 in / 1476 out tokens · 86551 ms · 2026-05-08T02:28:08.472444+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

13 extracted references · 6 canonical work pages · 1 internal anchor

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Therefore, we obtain wλ[ϕ] = Z d4xE −1 2 1 +λ α+O λ2 (∂µϕ)2 − Lnonlin (∂µϕ) ,(S19) where the nonlinear correctionLnonlin (∂µϕ)∼ O λ2

Here, by exploiting theO(4)symmetry of Euclidean spacetime, we obtain ⟨O(1) I ⟩0 = 0,⟨O (2) IJ ⟩0 ∝δ IJ .(S17) By analytically continuing the classical background field, we obtain dwλ[ϕ] dλ λ=0 =− α 2 Z d4xE (∂µϕ)2 ,(S18) whereαdenotes a constant. Therefore, we obtain wλ[ϕ] = Z d4xE −1 2 1 +λ α+O λ2 (∂µϕ)2 − Lnonlin (∂µϕ) ,(S19) where the nonlinear correc...