Mass of a quantum 't Hooft-Polyakov monopole

TL;DR

This paper non-perturbatively calculates the quantum mass of 't Hooft-Polyakov monopoles in the Georgi-Glashow model using lattice Monte Carlo simulations with twisted boundary conditions, exploring both weak and strong coupling regimes.

Contribution

It introduces a lattice Monte Carlo method with twisted boundary conditions to compute monopole masses non-perturbatively, including at strong coupling near the critical point.

Findings

Quantum corrections to classical monopole mass determined in weak coupling.

Method applicable to study monopole masses at strong coupling.

Hints of electric-magnetic duality near the critical point.

Abstract

The quantum mechanical mass of 't Hooft-Polyakov monopoles in the four-dimensional Georgi-Glashow is calculated non-perturbatively using lattice Monte Carlo simulations. This is done by imposing twisted boundary conditions that ensure there is one unit of magnetic charge on the lattice, and measuring the free energy difference between this ensemble and the vacuum. In the weak-coupling limit, the results can be used to determine the quantum correction to the classical mass, once renormalisation of couplings is taken properly into account. The methods can also be used to study the masses at strong coupling, i.e., near the critical point, where there are hints of a possible electric-magnetic duality.