Feynman Graph Integrals on ${\mathbb{C}}^d$

Abstract

We introduce a type of graph integrals which are holomorphic analogs of configuration space integrals. We prove their (ultraviolet) finiteness by considering a compactification of the moduli space of graphs with metrics, and study their failure to be holomorphic.

30 pages, 1 figure; Some typos have been corrected