Mass of a quantum 't Hooft-Polyakov monopole

Abstract

The quantum mechanical mass of 't Hooft-Polyakov monopoles in the fourdimensional 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.

’t Hooft-Polyakov monopoles in latticeSU(N)+adjoint Higgstheory

“…In particular, it will be straightforward to measure the monopole mass in the same way as in Ref. [13].…”

Nonperturbative study of the ’t Hooft-Polyakov monopole form factors

“…For simplicity, the parameters are the same as those of Ref. [15]. For these parameters, the theory has a second-order (or possibly very weakly first-order) phase transition at m 2 c % À0:27 between the confining phase at m 2 > m 2 c and the Coulomb phase at m 2 < m 2 c .…”

“…The conventional technique for studying magnetic monopoles and other topological defects with lattice Monte Carlo simulations has consisted of measuring their mass via their free energy [15,[24][25][26].…”

“…[15]) that affects the measurements of the monopole mass when the physical size of the monopole almost fills the box. The curve of the twist results changes concavity as the monopole becomes smaller than the box size.…”

“…These solutions have been studied extensively in classical field theory [12], but quantum results generally only exist in supersymmetric theories in which quantum corrections are straightforward. In nonsupersymmetric theories, results have been limited to leading logarithmic corrections to the monopole mass at the one-loop level [13,14], although the monopole mass has also been calculated nonperturbatively using numerical lattice field theory methods [15].…”