Feynman Graph Integrals on Kähler Manifolds

In this paper, we provide a rigorous proof of the convergence, in the Cauchy principal value sense, of Feynman graph integrals of holomorphic quantum field theories on closed real analytic Kähler manifolds. In the special case of Calabi-Yau manifolds, these graph integrals give rise to new invariants of Calabi-Yau metrics.