Gauge invariant extremization on the lattice

TL;DR

This paper develops a gauge-invariant extremization method for lattice gauge theories, enabling the identification of saddle points in a way that respects gauge symmetry, applicable to various gauge groups and actions.

Contribution

It introduces a gauge-invariant formulation of extremization on the lattice, improving upon previous gauge-variant approaches and applicable to multiple gauge groups and actions.

Findings

Formulated a gauge-invariant extremization method.

Applied the method to U(1) and SU(N) lattice gauge theories.

Demonstrated the method's applicability to standard plaquette actions.

Abstract

Recently, a method was proposed and tested to find saddle points of the action in simulations of non-abelian lattice gauge theory. The idea, called `extremization', is to minimize $\int(\dl S/\dl A_\mu)^2$. The method was implemented in an explicitly gauge variant way, however, and gauge dependence showed up in the results. Here we show how extremization can be formulated in a way that preserves gauge invariance on the lattice. The method applies to any gauge group and any lattice action. The procedure is worked out in detail for the standard plaquette action with gauge groups U(1) and SU(N).