Three dimensional large N monopole gas

TL;DR

This paper investigates the behavior of magnetic monopoles in a three-dimensional Yang-Mills/Higgs model at large N, revealing a hierarchy of monopole masses and a dilute gas structure influenced by eigenvalue distributions.

Contribution

It introduces a specific eigenvalue configuration that minimizes free energy and explores the resulting monopole mass hierarchy in the large N limit.

Findings

Monopoles exhibit a wide hierarchy of masses.

Some monopoles vanish as 1/N.

Dilute gas picture emerges in the large N limit.

Abstract

We study the large N limit in the presence of magnetic monopoles in the Yang-Mills/Higgs model in three dimensions. The physics in the limit depends strongly on the distribution of eigenvalues of the Higgs field in the vacuum, and we propose a particular, nondegenerate configuration. It minimizes the free energy at the moment of symmetry breaking. Given this, the magnetic monopoles show a wide hierarchy of masses, and some are vanishing as 1/N. The dilute gas picture, then, provides an interesting structure in the large N limit.