Monopole mass in the three-dimensional Georgi-Glashow model

Abstract

We study the three-dimensional Georgi-Glashow model to demonstrate how magnetic monopoles can be studied fully nonperturbatively 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 quantized '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 semiclassical predictions for the monopole. On large volumes we show that the free energy is screened to zero, signaling 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.