Momumentum Analyticity and Finiteness of Compactified String Amplitudes, Part I: Tori

TL;DR

This paper extends a superstring amplitude construction to compactified cases, addressing infrared divergences and tachyon contributions, and provides methods for obtaining finite amplitudes with explicit spectral representations.

Contribution

It introduces a framework for finite superstring amplitudes on tori, handling divergences and tachyons in compactified string theories, with explicit dispersion relation formulas.

Findings

Finite amplitudes expressed via dispersion relations

Resolution of infrared divergences in compactified strings

Handling of tachyon contributions in orbifold schemes

Abstract

We generalize to the case of compactified superstrings a construction given previously for critical superstrings of finite one loop amplitudes that are well-defined for all external momenta. The novel issues that arise for compactified strings are the appearance of infrared divergences from the propagation of massless strings in four dimensions and, in the case of orbifold schemes, the contribution of tachyons in partial amplitudes with given spin structure and twist sectors. Methods are presented for the resolution of these problems and expressions for finite amplitudes are given in terms of double and single dispersion relations, with explicit spectral densities.