Magnetic monopoles in 4D: a perturbative calculation

TL;DR

This paper investigates the definition and behavior of monopole creation operators in 3+1D gauge theories, revealing their dependence on Dirac strings and showing that their vacuum expectation value vanishes in perturbation theory, with nonperturbative effects expected to alter this.

Contribution

It provides a perturbative calculation of monopole operators in 4D gauge theories, highlighting their Dirac string dependence and the vanishing of their VEV in the confining phase.

Findings

Monopole creation operator depends on the Dirac string even in nonabelian theories.

The VEV of the monopole operator vanishes as system volume increases in perturbation theory.

Nonperturbative effects are expected to make the VEV finite by introducing an infrared cutoff.

Abstract

We address the question of defining the second quantised monopole creation operator in the 3+1 dimensional Georgi-Glashow model, and calculating its expectation value in the confining phase. Our calculation is performed directly in the continuum theory within the framework of perturbation theory. We find that, although it is possible to define the "coherent state" operator M(x) that creates the Coulomb magnetic field, the dependence of this operator on the Dirac string does not disappear even in the nonabelian theory. This is due to the presence of the charged fields (W^{\pm}). We also set up the calculation of the expectation value of this operator in the confining phase and show that it is not singular along the Dirac string. We find that in the leading order of the perturbation theory the VEV vanishes as a power of the volume of the system. This is in accordance with our naive expectation. We expect that nonperturbative effects will introduce an effective infrared cutoff on the calculation making the VEV finite.