Gauge theories on noncommutative Kähler manifolds

We study gauge theories on noncommutative homogeneous Kähler manifolds. To make the noncommutative manifolds, we use the deformation quantization with separation of variables for Kähler manifolds. We construct models of noncommutative gauge theories that are connected with usual Yang-Mills theories in the commutative limits. It is expected that the models connecting to commutative gauge theories are uniquely determined. As examples, we give noncommutative CP^N and noncommutative CH^N and gauge theories on them. Some kinds of gauge symmetry breaking and topological symmetry breaking by noncommutative deformations are observed by concrete geometrical calculations.