The monopole mass in the three-dimensional Georgi-Glashow model

TL;DR

This paper investigates magnetic monopoles in the three-dimensional Georgi-Glashow model using non-perturbative lattice Monte Carlo simulations, revealing how monopole free energy behaves across phases and resolving interpretative paradoxes.

Contribution

It provides the first non-perturbative lattice measurement of monopole free energy and clarifies its role as an order parameter in phase transitions.

Findings

Monopole free energy is non-zero in small volumes, matching semi-classical predictions.

In large volumes, monopole free energy is screened to zero, indicating monopole condensation.

The monopole mass cannot serve as a reliable order parameter due to screening effects.

Abstract

We study the three-dimensional Georgi-Glashow model to demonstrate how magnetic monopoles can be studied fully non-perturbatively in lattice Monte Carlo simulations, without any assumptions about the smoothness of the field configurations. We examine the apparent contradiction between the conjectured analytic connection of the `broken' and `symmetric' phases, and the interpretation of the mass (i.e., the free energy) of the fully quantised 't Hooft-Polyakov monopole as an order parameter to distinguish the phases. We use Monte Carlo simulations to measure the monopole free energy and its first derivative with respect to the scalar mass. On small volumes we compare this to semi-classical predictions for the monopole. On large volumes we show that the free energy is screened to zero, signalling the formation of a confining monopole condensate. This screening does not allow the monopole mass to be interpreted as an order parameter, resolving the paradox.