Large $N$ external-field quantum electrodynamics

TL;DR

This paper explores the large N limit of external-field quantum electrodynamics, showing that the all-loop contributions can be explicitly calculated for constant electromagnetic fields, providing new analytical insights into the theory.

Contribution

It demonstrates that in the large N limit, the Heisenberg-Euler effective action can be explicitly determined at any loop order for constant electromagnetic fields, including the all-orders strong field limit.

Findings

All-loop contributions are generated by the one-loop effective Lagrangian in constant fields.

Explicit all-orders strong field limit is derived for specific field configurations.

The approach simplifies the analysis of large N external-field QED.

Abstract

We advocate the study of external-field quantum electrodynamics with $N$ charged particle flavors. Our main focus is on the Heisenberg-Euler effective action for this theory in the large $N$ limit which receives contributions from all loop orders. The contributions beyond one loop stem from one-particle reducible diagrams. We show that specifically in constant electromagnetic fields the latter are generated by the one-loop Heisenberg-Euler effective Lagrangian. Hence, in this case the large $N$ Heisenberg-Euler effective action can be determined explicitly at any desired loop order. We demonstrate that further analytical insights are possible for electric-and magnetic-like field configurations characterized by the vanishing of one of the secular invariants of the electromagnetic field and work out the all-orders strong field limit of the theory.