The Monopole Equations in Topological Yang-Mills∗

We twist the monopole equations of Seiberg and Witten and show how these equations are realized in topological Yang-Mills theory. A Floer derivative and a Morse functional are found and are used to construct a unitary transformation between the usual Floer cohomologies and those of the monopole equations. Furthermore, these equations are seen to reside in the vanishing self-dual curvature condition of an OSp(1|2)-bundle. Alternatively, they may be seen arising directly from a vanishing self-dual curvature condition on an SU(2)-bundle in which the fermions are realized as spanning the tangent space for a specific background. CTP # 2397 December 1994 hep-th/9412206 This work is supported in part by funds provided by the U. S. Department of Energy (D.O.E.) under cooperative agreement #DE-FC02-94ER40818. Email: [email protected] Email: [email protected]