Disk Scattering of Open and Closed Strings (I)

TL;DR

This paper derives relations for disk scattering amplitudes involving open and closed strings, extending previous work by allowing different momenta for left- and right-movers, and reduces the computation to monodromy considerations.

Contribution

It extends the known relations for string scattering amplitudes to the disk world-sheet with different momenta for left- and right-movers of closed strings.

Findings

Derived disk amplitude relations involving open and closed strings.

Reduced amplitude computations to monodromy analysis on the world-sheet.

Extended previous double cover relations to the disk geometry.

Abstract

At the tree level, the scattering processes involving open and closed strings are described by a disk world-sheet with vertex operator insertions at the boundary and in the bulk. Such amplitudes can be decomposed as certain linear combinations of pure open string amplitudes. While previous relations have been established on the double cover (complex sphere) in this letter we derive them on the disk (upper complex half plane) allowing for different momenta of the left- and right-movers of the closed string. Formally, the computation of disk amplitudes involving both open and closed strings is reduced to considering the monodromies on the underlying string world-sheet.