Integrating topological degrees of freedom with perturbation theory in three dimensional Yang-Mills theory

Abstract

Polyakov has demonstrated that a monopole plasma gives confinement in Georgi Glashow model in three Euclidean dimensions. However his semi classical techniques are not applicable for pure YM 3 . Even though the gauge potential ansatz of 't Hooft Polyakov monopole has a finite action in YM 3 , it is not a stable classical solution, indeed, larger the 'size' smaller the action. We develop techniques for summing over such large overlapping monopole configurations. This is based on i) characterizing the configurations using eigenfunctions of B i (x) · B j (x), ii) obtaining a two potential formalism for Yang Mills theory. These techniques provide a way for combining renormalized perturbation theory and asymptotic freedom with confining effects of fluctuations of topological significance.