Vortices in SU(2) lattice gauge theory

TL;DR

This paper explores the properties and dynamics of thick vortices and monopoles in SU(2) lattice gauge theory, revealing their potential significance at large coupling parameters through measurements of free energy derivatives and potential energies.

Contribution

It introduces methods to create and analyze thick vortices and monopoles, providing new insights into their behavior and importance in the large beta limit of SU(2) gauge theory.

Findings

The free energy derivative of vortices decreases exponentially with cross-sectional area.

Thick and thin monopoles exhibit different potential energy behaviors.

Vortices and monopoles of increasing thickness are significant at large beta.

Abstract

We investigate some properties of thick vortices and thick monopoles in the SU(2) lattice gauge theory by inserting operators which create these excitations. Some quantities associated with the dynamical behaviour of thick vortices and thick monopoles are studied. 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 size. We also study the monopole-monopole potential energy for thick and thin monopoles. Our results suggest that vortices and monopoles of increasing thickness will play an important role in the large $\beta$ limit.