Topological Field Theory of Vortices over Closed Kahler Manifolds

By dimensional reduction, Einstein-Hermitian equations of n + 1 dimensional closed Kahler manifolds lead to vortex equations of n dimensional closed Kahler manifolds. A Yang-Mills-Higgs functional to unitary bundles over closed Kahler manifolds has topological invariance by adding the additional terms which have ghost fields. Henceforth we achieve the matter (Higgs field) coupled topological field theories in higher dimension.