Coupled equations for K\"ahler metrics and Yang-Mills connections
  We study equations on a principal bundle over a compact complex manifold coupling a connection on the bundle with a Kahler structure on the base. These equations generalize the conditions of constant scalar curvature for a Kahler metric and Hermite-Yang-Mills for a connection. We provide a moment map interpretation of the equations and study obstructions for the existence of solutions, generalizing the Futaki invariant, the Mabuchi K-energy and geodesic stability. We finish by giving some examples of solutions. 
Luis Alvarez-Consul, Mario Garcia-Fernandez and Oscar Garcia-Prada
math.DG hep-th math-ph math.AG math.MP math.SG