K\"ahler-Yang-Mills Equations and Vortices

TL;DR

This paper explores the geometry of K"ahler-Yang-Mills equations, their relation to vortex solutions, and their dimensional reductions, contributing to the understanding of complex geometric structures and gauge theories.

Contribution

It provides a review of the K"ahler-Yang-Mills equations and investigates their dimensional reductions related to vortex solutions, offering new insights into their geometric and analytical properties.

Findings

Analysis of the geometry of K"ahler-Yang-Mills equations

Connection between these equations and vortex solutions

Dimensional reduction techniques applied to the equations

Abstract

The K\"ahler-Yang-Mills equations are coupled equations for a K\"ahler metric on a compact complex manifold and a connection on a complex vector bundle over it. After briefly reviewing the main aspects of the geometry of the K\"ahler-Yang-Mills equations, we consider dimensional reductions of the equations related to vortices - solutions to certain Yang-Mills-Higgs equations.