Momentum Analyticity and Finiteness of the 1-Loop Superstring Amplitude

TL;DR

This paper develops an analytic continuation method for the 1-loop superstring amplitude, making it finite and well-defined, and analyzes its complex momentum plane singularities.

Contribution

It introduces a novel analytic continuation technique for superstring amplitudes, addressing divergence issues at 1-loop order.

Findings

Amplitude becomes finite after analytic continuation

Identifies poles and cuts in the complex momentum plane

Provides a framework for well-defined superstring amplitudes

Abstract

The Type II Superstring amplitude to 1-loop order is given by an integral of $\vartheta$-functions over the moduli space of tori, which diverges for real momenta. We construct the analytic continuation which renders this amplitude well defined and finite, and we find the expected poles and cuts in the complex momentum plane.