Deconfinement transition at weak coupling in Yang-Mills theory on a torus

Abstract

We describe a weak coupling realization of the deconfinement transition in gauge theory compactified on $R^3\times S^1$. We consider Yang-Mills theory with a single Weyl fermion of mass $m$ in the adjoint representation of the gauge group. The fermion is subject to periodic boundary conditions, $\lambda (0)=\lambda (L)$, where $L$ is the size of the circle $S_1$. This theory reduces to thermal Yang-Mills theory in the limit $m\to \infty$. In the limit $m\to 0$ the deconfinement transition can be studied using weak coupling methods. The analysis is based on semi-classical objects characterized by topological and magnetic charges. At leading order the relevant configurations are monopole-instantons and monopole-anti-monopole pairs ("bions"). We argue that in the $m-L$ plane the weak coupling transition is continuously connected to the deconfinement transition in pure gauge theory.

Comments: 7 pages, contribution to The 31th International Symposium on Lattice Field Theory - Lattice 2013, July 29-August 3, 2013