Vortices in SU(2) lattice gauge theory

TL;DR

This paper studies the properties of thick vortices and monopoles in SU(2) lattice gauge theory, revealing their potential significance at large coupling by analyzing free energy derivatives and interaction energies.

Contribution

It introduces methods to create and analyze thick vortices and monopoles, providing new insights into their behavior and importance in lattice gauge theory.

Findings

Free energy derivative decreases exponentially with vortex cross-sectional area.

Thick and thin monopoles exhibit distinct potential energy behaviors.

Vortices and monopoles may be crucial at large coupling regimes.

Abstract

We investigate some properties of thick vortices and thick monopoles in the SU(2) lattice gauge theory by inserting operators that create these excitations. We measure the derivative of the free energy of the vortex with respect to the coupling and we find that it falls exponentially with the cross sectional area of the vortex. We also study the monopole-monopole potential energy of thick and thin monopoles. Our results suggest that vortices and monopoles of increasing thickness will play an important role in the large $\beta$ limit.