Infrared physics of the $\mathrm{SU}(2)$ Georgi-Glashow crossover transition

TL;DR

This study investigates the phase transition in the three-dimensional SU(2) Georgi-Glashow model, focusing on monopole condensation, photon mass generation, and the validity of semiclassical relations at the nonperturbative level.

Contribution

The paper provides a lattice-based analysis of monopole effects and photon mass in the SU(2) Georgi-Glashow model, confirming semiclassical relations nonperturbatively.

Findings

Monopole density can be renormalised using gradient flow.

Photon mass correlates with monopole density as per Polyakov's relation.

Preliminary results support the semiclassical relation at the nonperturbative level.

Abstract

We perform a lattice study of the phase transition in the $\mathrm{SU}(2)$ Georgi-Glashow model in three dimensions, where the gauge symmetry is broken to $\mathrm{U}(1)$ by the Higgs mechanism and a photon-like state appears. Due to condensation of monopoles the photon acquires a mass, which depends on the number density of the monopoles. We show that the monopole density can be renormalised on the lattice using gradient flow. Our preliminary results suggest that Polyakov's semiclassical relation between the photon mass and the renormalised monopole density is valid also at the nonperturbative level.