The Monopole Equations in Topological Yang-Mills

Details The Monopole Equations in Topological Yang-Mills The Monopole Equations in Topological Yang-Mills

1994-12-22

arxiv.org/abs/hep-th/9412206v1

J.Math.Phys. 37 (1996) 1100-1105

Physics

High Energy Physics

High Energy Physics - Theory

7 pgs., LaTeX (fullpage)

Scientific paper

10.1063/1.531438

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.

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