Strong-field regime within effective field theory

TL;DR

This paper introduces a new method within effective field theory to accurately compute non-perturbative effects in strong background fields, demonstrated through scalar QED and relevant for understanding phenomena like Schwinger pair production.

Contribution

It develops a covariant derivative expansion-based approach to derive full second-derivative corrections in effective actions under strong fields, clarifying previous disagreements.

Findings

Derived the second-derivative corrections to the scalar Heisenberg--Euler effective action.

Showed the transseries structure of Schwinger pair production rate is preserved at this order.

Clarified discrepancies in coefficients of the effective action.

Abstract

Building upon the Covariant Derivative Expansion, we develop a method to compute effective actions that is able to capture non-perturbative effects induced by strong background fields. We demonstrate the method in scalar QED, by deriving the full second-derivative corrections to the scalar Heisenberg--Euler effective action. The corresponding result is interpreted as an effective field theory with three characteristic scales, two of which are large (mass and field strength) in comparison with the remaining one (derivatives of the field). As an application, we show that, at this order, the transseries structure of the Schwinger pair production rate is preserved, even if the involved coefficients are modified. Our analysis also helps clarify recent disagreements concerning the coefficients of this effective action.