Center vortices on SU(2) lattices

TL;DR

This paper demonstrates how gauge-invariant definitions of various center vortices on SO(3) x Z(2) configurations can be extended to SU(2), linking different vortex representations and analyzing their impact on quark potentials.

Contribution

It establishes a connection between vortex definitions in SO(3) x Z(2) and SU(2), showing how different representatives relate to projection vortices and gauge-invariant vortices.

Findings

Projection vortex counters approximate gauge-invariant ones.

Different SU(2) representatives reveal distinct vortex structures.

Vortex configurations influence static quark potentials.

Abstract

We show that gauge invariant definition of thin, thick and hybrid center vortices, defined by Kovacs and Tomboulis on SO(3) x Z(2) configurations, can also be defined in SU(2). We make this connection using the freedom of choosing a particular SU(2) representative of SO(3). We further show that in another representative the Tomboulis \sigma - \eta thin vortices are P (projection) vortices. The projection approximation corresponds to dropping the perimeter factor of a Wilson loop after appropriate gauge fixing. We present results for static quark potentials based on these vortex counters and compare pojection vortex counters with gauge invariant ones on the same configuration.