A New look at the vortex equations and dimensional reduction
Abstract
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×
P
1
.