Dirac monopoles embedded into SU(N) gauge theory with $\theta$ - term

TL;DR

This paper studies Dirac monopoles in SU(N) gauge theories with a theta-term, showing how they become dyons with specific representations and expressing the partition function as a vacuum average of Wilson loops.

Contribution

It introduces a novel representation of the SU(N) partition function with theta-term as a vacuum average of Wilson loops along monopole worldlines.

Findings

Monopoles acquire SU(N) charge and become dyons due to the theta-term.

Admitted monopole representations are explicitly enumerated.

Partition function expressed as vacuum average of Wilson loops.

Abstract

We consider Dirac monopoles embedded into SU(N) gauge theory with theta-term for $\theta = 4\pi M $ (where $M$ is half-integer for $N = 2$ and is integer for $N>2$). Due to the theta - term those monopoles obtain the SU(N) charge and become the dyons. They belong to different irreducible representations of SU(N) (but not to all of them). The admitted representations are enumerated. Their minimal rank increases with increasing of $N$. The main result of the paper is the representation of the partition function of SU(N) model with theta-term (that contains singular gauge fields correspondent to the mentioned monopoles) as the vacuum average of the product of Wilson loops (considered along the monopole worldlines). This vacuum average should be calculated within the correspondent model without theta-term.