Finiteness of multi-loop superstring amplitudes

TL;DR

This paper demonstrates that multi-loop superstring amplitudes are finite and modular invariant through a supermodular invariant regularization, confirming the cancellation of divergences in superstring theory.

Contribution

It introduces a supermodular invariant regularization method for divergent multi-loop superstring amplitudes and proves their finiteness and modular invariance.

Findings

Superstring amplitudes are explicitly finite after regularization.

Divergences cancel out in the superstring amplitudes.

Amplitudes are shown to be modular invariant.

Abstract

Superstring amplitudes of an arbitrary genus are calculated through super-Schottky parameters by a summation over the fermion strings. For a calculation of divergent multi-loop fermion string amplitudes a supermodular invariant regularization procedure is used. A cancellation of divergences in the superstring amplitudes is established. Grassmann variables are integrated, the superstring amplitudes are obtained to be explicitly finite and modular invariant.