Notes on reductions of superstring theory to bosonic string theory

TL;DR

This paper explores the complexities of integrating over odd moduli in superstring theory and identifies cases where these issues simplify, linking superstring and bosonic string theories through specific embeddings and amplitude relations.

Contribution

It analyzes conditions under which the integration over odd moduli simplifies, clarifying the relationship between superstring and bosonic string theories in certain cases.

Findings

Simplification of odd moduli integration in specific superstring cases

Connection between N=0 and N=1 string theories via embedding

Relation between graviphoton and topological string amplitudes

Abstract

It is in general very subtle to integrate over the odd moduli of super Riemann surfaces in perturbative superstring computations. We study how these subtleties go away in favorable cases, including the embedding of N=0 string to N=1 string by Berkovits and Vafa, and the relation of the graviphoton amplitude and the topological string amplitude by Antoniadis, Gava, Narain and Taylor and Bershadsky, Cecotti, Ooguri and Vafa. The Poincar\'e dual of the moduli space of Riemann surfaces in the moduli space of super Riemann surfaces plays an important role.