Gauge Invariant Quark Propagator in the Instanton Background

TL;DR

This paper compares different gauge choices for the quark propagator in an instanton background and introduces a gauge-invariant propagator that yields a finite quark condensate without infrared cutoff.

Contribution

It presents a gauge-invariant quark propagator in an instanton background, avoiding infrared cutoff and providing a more consistent approach to quark condensate calculations.

Findings

Gauge-invariant propagator matches regular and singular gauge results

Finite quark condensate obtained without infrared cutoff

Analysis informs better gauge choices in instanton models

Abstract

After a general discussion on the choice of gauge, we compare the quark propagator in the background of one instanton in regular and singular gauge with a gauge invariant propagator obtained by inserting a path-ordered gluon exponential. Using a gauge motivated by this analysis, we were able to obtain a finite result for the quark condensate without introducing an infrared cutoff nor invoking some instanton model.