Instantons and Gribov Copies in the Maximally Abelian Gauge

TL;DR

This paper investigates the Faddeev-Popov operator in the maximally Abelian gauge for SU(N), finds explicit zero modes in SU(2), and discusses the physical implications of instantons as horizon configurations.

Contribution

It provides an explicit analytic zero mode solution of the Faddeev-Popov operator in the background of an instanton, linking instantons to horizon configurations in the gauge.

Findings

Explicit zero mode in SU(2) instanton background

Instantons correspond to horizon configurations in the gauge

Analytic solutions in a toy model and field theory case

Abstract

We calculate the Faddeev-Popov operator corresponding to the maximally Abelian gauge for gauge group SU(N). Specializing to SU(2) we look for explicit zero modes of this operator. Within an illuminating toy model (Yang-Mills mechanics) the problem can be completely solved and understood. In the field theory case we are able to find an analytic expression for a normalizable zero mode in the background of a single `t Hooft instanton. Accordingly, such an instanton corresponds to a horizon configuration in the maximally Abelian gauge. Possible physical implications are discussed.