Euler-Heisenberg actions in higher dimensions

TL;DR

This paper generalizes the Euler-Heisenberg effective action to higher dimensions using Schwinger's formalism, providing explicit formulas in six dimensions and analyzing pair production and Weyl anomalies.

Contribution

It introduces a method to compute one-loop effective actions in higher-dimensional QED and presents the explicit six-dimensional Euler-Heisenberg action.

Findings

Closed form expression for six-dimensional Euler-Heisenberg action

Analysis of pair production in higher dimensions

Identification of a conformal primary field related to Weyl anomaly

Abstract

We extend Schwinger's proper-time formalism to provide a method for computing the one-loop effective action for both spinor and scalar quantum electrodynamics in $d=2n>4$ dimensions. The closed form expression for the six-dimensional Euler-Heisenberg action is given, along with a subsequent analysis of pair production in $d$ dimensions. In the $d=6$ case, we present a composite conformal primary field of dimension $+6$ which determines the contribution of the electromagnetic field to the Weyl anomaly in curved space.