Bounds on nonlinear effective field theories via resurgent relative entropy

TL;DR

This paper develops bounds on nonlinear effective field theories using resurgent relative entropy, linking nonperturbative effects and stability conditions through analytic continuation in fermionic QED.

Contribution

It introduces a novel approach employing resummed relative entropy to constrain EFT coefficients and identify instabilities, including the Schwinger effect.

Findings

Resummed relative entropy fixes the sign of EFT coefficient growth.

Violation of the entropy bounds indicates nonperturbative instabilities.

Application to fermionic QED demonstrates the Schwinger effect as a stability criterion.

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.