't Hooft surface in lattice gauge theory

TL;DR

This paper develops a lattice formulation for the 't Hooft surface, a topological vortex world sheet, and demonstrates its calculation in Abelian and non-Abelian Higgs models, including a specific vortex potential computation.

Contribution

It introduces formulas for calculating the 't Hooft surface expectation value in lattice gauge theories, including non-Abelian models, and applies them to compute vortex interactions.

Findings

Derived formulas for 't Hooft surface expectation values

Computed intervortex potential in charge-2 Abelian Higgs model

Demonstrated the approach in non-Abelian Higgs models

Abstract

We discuss the lattice formulation of the 't Hooft surface, that is, the two-dimensional surface operator of a dual variable. The 't Hooft surface describes the world sheets of topological vortices. We derive the formulas to calculate the expectation value of the 't Hooft surface in the multiple-charge lattice Abelian Higgs model and in the lattice non-Abelian Higgs model. As the first demonstration of the formula, we compute the intervortex potential in the charge-2 lattice Abelian Higgs model.