S-matrix element of two R-R and one NS states

TL;DR

This paper computes a specific string scattering amplitude involving R-R and NS states, verifies duality symmetries, and proposes a soft theorem for disk-level amplitudes with multiple strings.

Contribution

It provides an explicit calculation of a mixed R-R and NS string amplitude, demonstrates its duality properties, and introduces a new soft theorem for open-closed string scattering.

Findings

Amplitude satisfies duality Ward identities

Amplitude transforms under S-duality to known configurations

Proposed soft theorem is satisfied by the calculated amplitude

Abstract

We explicitly calculate the disk-level S-matrix element of two closed string R-R and one open string NS vertex operators in RNS formalism. We show that the amplitude satisfies various duality Ward identities. In particular, when one of the R-R is zero-form, the other one is two-form and the NS state is gauge boson, the amplitude transforms under S-duality Ward identity to the amplitude of one dilaton, one B-field and one gauge boson which has been recently calculated explicitly. We have also proposed a soft theorem for disk-level scattering amplitude of arbitrary number of hard closed strings and one soft open string at the leading order of soft momentum, and shown that the above amplitude satisfies the soft theorem.