Real topological string amplitudes

TL;DR

This paper explores the computation of real topological string amplitudes via physical superstring correlation functions in type I and orientifolded type II theories, establishing their relation to holomorphic derivatives of topological amplitudes.

Contribution

It demonstrates that physical superstring correlators precisely compute the holomorphic derivatives of real topological string amplitudes and extends this result to the standard closed oriented case.

Findings

Correlation functions match derivatives of topological amplitudes

Results apply to both real topological strings and standard cases

Provides a new method for computing topological string amplitudes

Abstract

We discuss the physical superstring correlation functions in type I theory (or equivalently type II with orientifold) that compute real topological string amplitudes. We consider the correlator corresponding to holomorphic derivative of the real topological amplitude $G_\chi$, at fixed worldsheet Euler characteristic $\chi$. This corresponds in the low-energy effective action to N=2 Weyl multiplet, appropriately reduced to the orientifold invariant part, and raised to the power $g'=-\chi+1$. We show that the physical string correlator gives precisely the holomorphic derivative of topological amplitude. Finally, we apply this method to the standard closed oriented case as well, and prove a similar statement for the topological amplitude $F_g$.