Gauge invariant extremization

TL;DR

This paper develops a gauge invariant formulation of extremization for lattice gauge theories, enabling the identification of saddle points without gauge dependence, applicable to various gauge groups and actions.

Contribution

It introduces a gauge invariant extremization method for lattice gauge theories, improving upon previous gauge-variant approaches.

Findings

Formulation detailed for U(1) and SU(N) gauge theories

Method applicable to any gauge group and lattice action

Addresses gauge dependence in extremization procedures

Abstract

Recently, Duncan and Mawhinney introduced a method to find saddle points of the action in simulations of non-abelian lattice gauge theory. The idea, called `extremization', is to minimize $\int(\delta S/\delta A_\mu)^2$ instead of the action $S$ itself as in conventional `cooling'. The method was implemented in an explicitly gauge variant way, however, and gauge dependence showed up in the results. Here we present a gauge invariant formulaton of extremization on the lattice, applicable to any gauge group and any lattice action. The procedure is worked out in detail for U(1) and SU(N) lattice gauge theory with the plaquette action.