Real 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 $F_g$.