Magnetic monopoles in the high temperature phase of Yang-Mills theories

TL;DR

This study examines the properties and interactions of thermal abelian magnetic monopoles in high-temperature SU(2) Yang-Mills theories, revealing a non-trivial temperature dependence and gauge effects.

Contribution

It provides the first detailed lattice investigation of thermal monopoles' density, correlations, and gauge dependence in high-temperature Yang-Mills theories.

Findings

Monopole density has a well-defined continuum limit.

Temperature dependence deviates from free particle gas predictions.

Non-trivial interactions among monopoles are observed.

Abstract

We investigate the properties of thermal abelian magnetic monopoles in the high temperature phase of Yang--Mills theories, following a recent proposal for their identification on lattice configurations. The study is done for SU(2) pure gauge theory, for temperatures going up to about 10 times the deconfining temperature and using the Maximal Abelian gauge to perform the abelian projection. We find that the monopole density has a well defined continuum limit. Its temperature dependence disagrees with a free particle gas prediction and is instead well described by a $T^3/(\log (T/\Lambda))^\alpha$ behaviour in all the explored range, with $\alpha \sim 2$ and $\Lambda \sim 100$ MeV. Also the study of spatial correlations of thermal monopoles shows the presence of non-trivial interactions among them. Finally, we discuss the gauge dependence of our results, showing that it is significant and that, even within the Maximal Abelian gauge, Gribov copy effects are important.