Zero modes, beta functions and IR/UV interplay in higher-loop QED

TL;DR

This paper investigates the connection between short-distance quantum field theory behavior and strong-field limits in QED, emphasizing the importance of zero modes and IR/UV interplay at two loops in self-dual backgrounds.

Contribution

It reveals the crucial role of zero modes in two-loop QED effective Lagrangians and provides a new derivation, highlighting differences from one-loop instanton physics.

Findings

Zero modes significantly affect two-loop QED calculations.

A new derivation of two-loop effective Lagrangians is presented.

The IR/UV interplay differs at two loops compared to one-loop analysis.

Abstract

We analyze the relation between the short-distance behavior of quantum field theory and the strong-field limit of the background field formalism, for QED effective Lagrangians in self-dual backgrounds, at both one and two loop. The self-duality of the background leads to zero modes in the case of spinor QED, and these zero modes must be taken into account before comparing the perturbative beta function coefficients and the coefficients of the strong-field limit of the effective Lagrangian. At one-loop this is familiar from instanton physics, but we find that at two-loop the role of the zero modes, and the interplay between IR and UV effects in the renormalization, is quite different. Our analysis is motivated in part by the remarkable simplicity of the two-loop QED effective Lagrangians for a self-dual constant background, and we also present here a new independent derivation of these two-loop results.