On moduli spaces of flat connections with non-simply connected structure group

We consider the moduli space of flat G-bundles over the two-dimensional torus, where G is a real, compact, simple Lie group which is not simply connected, We show that the connected components that describe topologically non-trivial bundles are isomorphic as symplectic spaces to moduli spaces of topologically trivial bundles with a different structure group, Some physical applications of this isomorphism which allows one to trade topological non-triviality for a change of the gauge group are sketched. (C) 1997 Elsevier Science B.V.