Potential energy of Yang-Mills vortices in three and four dimensions

TL;DR

This paper calculates the energy of Yang-Mills vortices in 3D and 4D using 1-loop approximation, revealing the dynamical preference for Z(2) vortices and comparing with Polyakov line potentials.

Contribution

It provides a detailed calculation of vortex energies as functions of flux and Wilson loops, highlighting the dynamical favorability of Z(2) vortices.

Findings

Quantized Z(2) vortices are energetically preferred.

Vortices with arbitrary fluxes are not ruled out.

Comparison with Polyakov line potential at nonzero temperature.

Abstract

We calculate the energy of a Yang-Mills vortex as function of its magnetic flux or, else, of the Wilson loop surrounding the vortex center. The calculation is performed in the 1-loop approximation. A parallel with a potential as function of the Polyakov line at nonzero temperatures is drawn. We find that quantized Z(2) vortices are dynamically preferred though vortices with arbitrary fluxes cannot be ruled out.