Fermion-induced quantum action of vortex systems

TL;DR

This paper investigates the quantum effects of fermions in vortex backgrounds across 2+1 and 3+1 dimensions, using worldline numerics to analyze interactions, mass dependence, and chiral condensates, revealing limits of traditional analytical methods.

Contribution

It introduces a detailed numerical analysis of fermion-induced quantum actions in vortex systems, including vortex interactions and chiral condensate formation, extending understanding beyond the derivative expansion approximation.

Findings

Quantum action depends on fermion mass and vortex flux.

Binary-vortex interactions are quantitatively computed.

Insights into the limits of the derivative expansion.

Abstract

The quantum action generated by fermions which are minimally coupled to abelian vortex background fields is studied in D=2+1 and D=3+1 Euclidean dimensions. We present a detailed analysis of single- and binary-vortex configurations using the recently developed method of worldline numerics. The dependence of the fermion-induced quantum action on the fermion mass and the magnetic fluxes carried by the vortices is studied, and the binary-vortex interaction is computed. Additionally, we discuss the chiral condensate generated from a dilute gas of vortices in the intermediate fermion mass range for the case D=3+1. As a byproduct, our findings provide insight into the validity limits of the derivative expansion, which is the standard analytical approach to inhomogeneous backgrounds.