Abelian spatial string tension in finite temperature SU(2) gauge theory

TL;DR

This study demonstrates Abelian dominance in spatial string tension in finite temperature SU(2) gauge theory without gauge fixing, showing monopole contributions are significant and that dimensional reduction applies above twice the critical temperature.

Contribution

It provides the first lattice evidence of Abelian dominance and monopole contributions to spatial string tension without gauge fixing in finite temperature SU(2) gauge theory.

Findings

Abelian and non-Abelian spatial string tensions agree within errors, indicating Abelian dominance.

Monopole contributions can be nearly as large as non-Abelian and Abelian ones.

Dimensional reduction holds for both sectors at temperatures above twice the critical temperature.

Abstract

We investigate Abelian and monopole contributions to spatial string tension in the deconfined phase of finite temperature SU(2) gauge theory without imposing any gauge fixing conditions. Lattice calculations of non-Abelian and Abelian spatial string tensions from the Wilson action at gauge coupling $\beta=2.74$ and lattice volume $24^3\times{N_t}$ $(N_{t}=\left\{ 24,8,6,4,2)\right\}$ show that these string tensions agree with each other within error bars at any adopted value of $N_t$, which implies Abelian dominance. From measurements of non-Abelian, Abelian, and monopole forces that arise from the corresponding spatial string tension, furthermore, we find the tendency that the monopole contribution to the spatial string tension can be almost as large as the non-Abelian and Abelian ones. The temperature dependence of the calculated non-Abelian and Abelian spatial string tensions allows us to conclude that the concept of dimensional reduction holds both for non-Abelian and Abelian sectors at temperatures higher than twice the critical temperature.