Considerations about Gribov ambiguities for the abelian Higgs model in the presence of chemical potential and temperature

TL;DR

This paper investigates how a chemical potential affects Gribov ambiguities in a U(1) gauge theory at finite temperature, showing that the chemical potential reduces the solutions for gauge fixing ambiguities and providing explicit solutions at zero temperature.

Contribution

It demonstrates that chemical potential suppresses Gribov copies in a U(1) theory and derives explicit solutions at zero temperature, extending understanding of gauge fixing at finite density.

Findings

Chemical potential restricts solutions to the Gribov problem.

Explicit solutions found at zero temperature as functions of chemical potential.

Finite temperature solutions satisfy KMS boundary conditions.

Abstract

In this letter we discuss the influence of a U(1) chemical potential $\mu$ on the existence of Gribov copies in a U(1) theory at finite temperature $T$. We show that the chemical potential conspires against the existence of Gribov copies in the sense that it restricts the space of solutions of the consistency equation for the gauge parameter. Explicit solutions are found for T=0, as function of $\mu$. In the finite temperature case we find also a class of solutions which satisfy the KMS boundary conditions in the euclidean time direction, having also a vanishing behavior when $|\mathbf r|\to\infty$