Non-abelian monopoles and vortices

Details Non-abelian monopoles and vortices Non-abelian monopoles and vortices

1996-02-09

arxiv.org/abs/alg-geom/9602010v2

Mathematics

Algebraic Geometry

Revised version, in which some minor clarrifications and a number of unjustly ommitted references have been added. (Apologies

Scientific paper

The Seiberg-Witten equations are defined on certain complex line bundles over smooth oriented four manifolds. When the base manifold is a complex Kahler surface, the Seiberg-Witten equations are essentially the Abelian vortex equations. Using known non-abelian generalizations of the vortex equations as a guide, we explore some non-abelian versions of the Seiberg-Witten equations. We also make some comments about the differences between the vortex equations that have previously appeared in the literature and those that emerge as Kahler versions of Seiberg-witten type equations.

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