Full mass range analysis of the QED effective action for an O(2)xO(3) symmetric field

TL;DR

This paper performs a comprehensive numerical analysis of the QED effective action for O(2)xO(3) symmetric fields across all mass ranges, revealing the role of anomalies and confirming theoretical conjectures.

Contribution

It introduces the partial-wave-cutoff method for full mass range analysis of the QED effective action in symmetric backgrounds, including massless limits and anomaly effects.

Findings

Matched asymptotics with inverse mass expansion at large masses

Obtained stable numerical results in the massless limit

Identified the dominance of the anomaly term in small-mass behavior

Abstract

An interesting class of background field configurations in quantum electrodynamics (QED) are the O(2)xO(3) symmetric fields, originally introduced by S.L. Adler in 1972. Those backgrounds have some instanton-like properties and yield a one-loop effective action that is highly nontrivial, but amenable to numerical calculation. Here, we use the recently developed "partial-wave-cutoff method" for a full mass range numerical analysis of the effective action for the "standard" O(2)xO(3) symmetric field, modified by a radial suppression factor. At large mass, we are able to match the asymptotics of the physically renormalized effective action against the leading two mass levels of the inverse mass expansion. For small masses, with a suitable choice of the renormalization scheme we obtain stable numerical results even in the massless limit. We analyze the N - point functions in this background and show that, even in the absence of the radial suppression factor, the two-point contribution to the effective action is the only obstacle to taking its massless limit. The standard O(2)xO(3) background leads to a chiral anomaly term in the effective action, and both our perturbative and nonperturbative results strongly suggest that the small-mass asymptotic behavior of the effective action is, after the subtraction of the two-point contribution, dominated by this anomaly term as the only source of a logarithmic mass dependence. This confirms a conjecture by M. Fry.