Topological Yang–Mills theory from non-commutative geometry

Abstract

It will be shown that the topological Yang–Mills theory of Witten can be induced from the usual Yang–Mills theory of the second rank antisymmetric tensor field when the matrix derivative of non-commutative geometry proposed by Connes is incorporated in the superconnection framework. It is done by identifying consistently the antisymmetric tensor field B with the usual field strength F by B=−F.