Energy Density of Vortices in the Schroedinger Picture

TL;DR

This paper calculates the one-loop energy density of magnetic vortices in SU(2) Yang-Mills theory using the Schrödinger picture, considering gluonic and quark fluctuations, and analyzes their stability and energy landscape.

Contribution

It provides a novel calculation of vortex energy density including fermionic effects, revealing how fermions lift degeneracy with the perturbative vacuum.

Findings

Fermions increase vortex energy, breaking degeneracy.

Center vortices are local minima in the effective potential.

Energy density depends on magnetic flux.

Abstract

The one-loop energy density of an infinitely thin static magnetic vortex in SU(2) Yang-Mills theory is evaluated using the Schroedinger picture. Both the gluonic fluctuations as well as the quarks in the vortex background are included. The energy density of the magnetic vortex is discussed as a function of the magnetic flux. The center vortices correspond to local minima in the effective potential. These minima are degenerated with the perturbative vacuum if the fermions are ignored. Inclusion of fermions lifts this degeneracy, raising the vortex energy above the energy of the perturbative vacuum.