Three dimensional large N monopole gas

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.