Topological defects in lattice gauge theories

TL;DR

This paper introduces a non-perturbative method to measure defect free energies in lattice gauge theories, enabling phase distinction and monopole mass calculation without gauge fixing.

Contribution

It develops a formalism connecting defect free energies with 't Hooft loops, applicable to various gauge theories and phases, without relying on local order parameters.

Findings

Defines defect free energies via twisted boundary conditions.

Allows phase discrimination in gauge theories.

Provides monopole mass measurement without gauge fixing.

Abstract

We present a non-perturbative formalism for measuring defect free energies (monopole mass or vortex tension) in three-dimensional SU(2)+adjoint Higgs models. Starting from twisted, translation invariant boundary conditions, we perform a change of variables that allows us to express the defect free energies in terms of 't Hooft loops. We propose that the defect free energies can be used to distinguish between phases in this model, and also more generally in other gauge field theories where no local order parameters exist. In the case of monopoles, our construction can also be used in four-dimensional pure-gauge SU(2) theory, where it gives the monopole mass in the maximally Abelian gauge without the need of actually fixing the gauge in the simulation. Moreover, the expression is manifestly independent of the choice of the Abelian projection as long as it is compatible with the classical 't Hooft-Polyakov solution.