# Dual vortices and gauge choice in Abelian projected SU(2) lattice gauge theory

## TL;DR

This paper investigates vortex formation in Abelian projected SU(2) lattice gauge theory, comparing different gauge choices and their implications for understanding confinement, highlighting the maximal Abelian gauge as the most effective for this purpose.

## Contribution

It compares vortex formation in Polyakov and maximal Abelian gauges, establishing the latter as the preferred gauge for modeling confinement in SU(2) lattice gauge theory.

## Key findings

- Vortices are observed in the Polyakov projection, linking dual superconductor order parameters to vortex existence.
- The Polyakov Abelian projection has limitations, making the maximal Abelian projection more suitable.
- A non-zero monopole field expectation value signals confinement in both gauges.

## Abstract

We explore vortex formation for Abelian projected SU(2) in the Polyakov gauge and compare the results with those calculated in the maximal Abelian gauge. In both gauges, a non-zero vacuum expectation value of a monopole field operator signals confinement. We find vortices in the Polyakov projection, confirming the connection between the dual superconductor order parameter and the existence of vortices. However we find that the Polyakov Abelian projection is problematic, leaving the maximal Abelian projection as the best candidate to define an effective theory of confinement in this scenario.