Monopole condensates in SU(N) Yang-Mills Theory

Abstract

Faddeev and Niemi have proposed a reformulation of SU(2) Yang-Mills theory in terms of new variables, appropriate for describing the theory in its infrared limit based on the intuitive picture of colour confinement due to monopole condensation. I generalize their proposal (with some differences) to SU(N) Yang-Mills theory. The natural variables are $N-1$ mutually commuting traceless $N\times N$ Hermitian matrices, an element of the maximal torus defined by these commuting matrices, $N-1$ Abelian gauge fields for the maximal torus gauge group, and an invariant symmetric two-index tensor on the tangent space of the maximal torus, adding up to the requisite 2$(N^{2}-1)$ physical degrees of freedom.