The other topological twisting of N = 4 Yang-Mills Original Research Article

We present the alternative topological twisting of N = 4 Yang-Mills, in which the path integral is dominated not by instantons, but by flat connections of the complexified gauge group. The theory is non-trivial on compact orientable four-manifolds with non-positive Euler number, which are necessarily not simply connected. On such manifolds, one finds a single topological invariant, analogous to the Casson invariant of three-manifolds.