Multiloop World-Line Green Functions from String Theory

Abstract

We show how the multiloop bosonic Green function of closed string theory reduces to the world-line Green function as defined by Schmidt and Schubert in the limit where the string world-sheet degenerates into a $\Phi^3$ particle diagram. To obtain this correspondence we have to make an appropriate choice of the local coordinates defined on the degenerate string world sheet. We also present a set of simple rules that specify, in the explicit setting of the Schottky parametrization, which is the corner of moduli space corresponding to a given multiloop $\Phi^3$ diagram.