Monopoles, Polyakov loops, and gauge fixing on the Torus - Ford, Chris; Pawlowski, Jan M. (Annals of physics, 2002)
We consider pure Yang-Mills theory on the four torus. A set of non-Abelian transition functions which encompass all instanton sectors is presented. It is argued that these transition functions are a convenient starting point for gauge fixing. In particular, we give an extended Abelian projection with respect to the Polyakov loop, whereA0is independent of time and in the Cartan subalgebra. In the non-perturbative sectors such gauge fixings are necessarily singular. These singularities can be restricted to Dirac strings joining monopole and anti-monopole like “defects”.