The other topological twisting of N=4 Yang-Mills

Abstract

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 nontrivial on compact orientable four-manifolds with nonpositive 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.Comment: 19 (big), 13 (little) pages, LaTeX. (Type b or l when prompted.) Files are also available from http://www.tau.ac.il/~neil/links/papers/flat/ or http://www.tau.ac.il/~neilm/.Me/papers/flat