Monopoles, Polyakov-Loops and Gauge Fixing on the Torus

Abstract

We consider pure Yang Mills theory on the four torus. A set of non-Abelian transition functions is presented which encompass all instanton sectors. 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, where $A_0$ is 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''.

24 pages, 4 figures, Latex 2e, some minor improvements

References in corpus (1)

• Resolution of Gauss' law in Yang-Mills theory by Gauge Invariant Projection: Topology and Magnetic Monopoles

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