Topological Amplitudes in String Theory

TL;DR

This paper demonstrates that certain genus g type II string amplitudes are described by topological partition functions, linking them to effective actions and holomorphic anomalies in string theory.

Contribution

It establishes a connection between genus g string amplitudes and topological partition functions, extending the understanding of holomorphic anomalies in string theory.

Findings

Genus g amplitudes are given by topological partition functions F_g.

These amplitudes contribute to four-dimensional effective actions as sum of F_g W^{2g}.

Holomorphic anomaly of F_g relates to non-localities from massless state propagation.

Abstract

We show that certain type II string amplitudes at genus $g$ are given by the topological partition function $F_g$ discussed recently by Bershadsky, Cecotti, Ooguri and Vafa. These amplitudes give rise to a term in the four-dimensional effective action of the form $\sum_g F_g W^{2g}$, where $W$ is the chiral superfield of $N=2$ supergravitational multiplet. The holomorphic anomaly of $F_g$ is related to non-localities of the effective action due to the propagation of massless states. This result generalizes the holomorphic anomaly of the one loop case which is known to lead to non-harmonic gravitational couplings.