2+1 d Georgi Glashow Model Near Critical Temperature

TL;DR

This paper analyzes the behavior of magnetic vortices and Polyakov loops in the 2+1D Georgi-Glashow model near the deconfining transition, revealing significant vortex correlations and symmetry breaking effects.

Contribution

It provides an explicit fermionic representation to compute vortex and Polyakov loop correlators near the critical temperature, highlighting the role of magnetic vortices in symmetry breaking.

Findings

The VV correlator is large near the transition.

Magnetic vortices contribute significantly to entropy and free energy.

Magnetic U(1) symmetry breaking is an order one effect near criticality.

Abstract

We study correlations functions of magnetic vortices $V$ and Polyakov loop $P$ operators in the 2+1 dimensional Georgi-Glashow model in the vicinity of the deconfining phase transition. In this regime the (dimensionally reduced) model is mapped onto a free theory of two massive Majorana fermions. We utilize this fermionic representation to explicitly calculate the expectation values of $V$ and $P$ as well as their correlators. In particular we show that the $VV$ correlator is large, and thus the anomalous breaking of the magnetic $U(1)$ symmetry is order one effect in the near critical region. We also calculate the contribution of magnetic vortices to the entropy and the free energy of the system.