A New look at the vortex equations and dimensional reduction
Loading...
Date
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
In order to use the technique of dimensional reduction, it is usually necessary for there to be a symmetry coming from a group action. In this paper we consider a situation in which there is no such symmetry, but in which a type of dimensional reduction is nevertheless possible. We obtain a relation between the Coupled Vortex equations on a closed Kahler manifold, $X$, and the Hermitian-Einstein equations on certain $P^1$-bundles over $X$. Our results thus generalize the dimensional reduction results of Garcia-Prada, which apply when the Hermitian-Einstein equations are on $X\times P^1$.
23 pages, AMSTeX, to be published in the Proceedings of the First USA/Brazil Workshop on Geometry, Topology and Physics, held in Campinas, Brazil, June 1996
23 pages, AMSTeX, to be published in the Proceedings of the First USA/Brazil Workshop on Geometry, Topology and Physics, held in Campinas, Brazil, June 1996