Resurgence of the effective action in inhomogeneous fields

We show how background field inhomogeneities modify the nonperturbative structure of the effective action. The simple Borel poles of the Euler-Heisenberg effective action become branch points, and new branch points also appear, indicating new nonperturbative effects. This information is resurgently encoded in the perturbative weak field expansion and becomes physically significant for strongly inhomogeneous fields. We also show that resurgent extrapolation methods permit the decoding of a surprising amount of nonperturbative information from a relatively modest amount of perturbative input, enabling accurate analytic continuations from weak field to strong field, and of a spatially dependent magnetic background to a time dependent electric background. These extrapolations are far superior to standard Wentzel-Kramers-Brillouin approximation and locally constant-field approximations.

Automated summary

This article demonstrates how the nonperturbative structure of the effective action is modified by background field inhomogeneities. The simple Borel poles of the Euler-Heisenberg effective action turn into branch points, and new branch points appear, indicating new nonperturbative effects. This information is encoded in the perturbative weak field expansion and becomes significant for strongly inhomogeneous fields. The article also shows that resurgent extrapolation methods allow the extraction of a significant amount of nonperturbative information from a relatively small perturbative input, enabling accurate analytic continuations from weak field to strong field and from spatially dependent magnetic background to time dependent electric background. These extrapolations are superior to standard Wentzel-Kramers-Brillouin approximation and locally constant-field approximations.