Topological contents of 3D Seiberg-Witten theory

Details Topological contents of 3D Seiberg-Witten theory Topological contents of 3D Seiberg-Witten theory

1997-09-03

arxiv.org/abs/hep-th/9709026v1

Physics

High Energy Physics

High Energy Physics - Theory

8 pages, 7 Postscript figures, uses plenum and epsfig, talk at the NATO Advanced Research Workshop: "Recent Developments in Qu

Scientific paper

Using physical arguments (Higgs mechanism, superconductivity, infrared regime, duality) and a geometric-topological construction (scalar curvature distribution compatible with surgery), we propose a topological interpretation of 3D SW theory in terms of the abelian Casson invariant. Further algebraic reasoning shows equivalence of that invariant to the Alexander ``polynomial''. Our starting point is a 3D version of the original SW theory. Observing that the scalar curvature $R$ plays the role of a mass-squared parameter for the monopole field we can use that observation to control the theory in low-energy limit.

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