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.
- Pub Date:
- February 1996
- Mathematics - Algebraic Geometry;
- Mathematics - Differential Geometry
- Revised version, in which some minor clarrifications and a number of unjustly ommitted references have been added. (Apologies to any inadvertantly offended parties.) To appear in the Proceedings of the 1995 Aarhus Conference in Geometry and Physics. 25 pages. AMSLaTeX v 2.09