KLT Factorization of Winding String Amplitudes

TL;DR

This paper demonstrates a KLT-type factorization of closed string amplitudes with winding and momentum in toroidal compactifications into open string amplitudes, revealing a deep connection between closed and open string states.

Contribution

It introduces a novel factorization of closed string amplitudes into open string amplitudes in toroidal compactifications, linking winding and momentum quantum numbers to open string configurations.

Findings

Closed string amplitudes factorize into open string amplitudes.

Winding and momentum quantum numbers map to open string winding numbers.

The factorization relates closed string states to open string D-brane configurations.

Abstract

We uncover a Kawai-Lewellen-Tye (KLT)-type factorization of closed string amplitudes into open string amplitudes for closed string states carrying winding and momentum in toroidal compactifications. The winding and momentum closed string quantum numbers map respectively to the integer and fractional winding quantum numbers of open strings ending on a D-brane array localized in the compactified directions. The closed string amplitudes factorize into products of open string scattering amplitudes with the open strings ending on a D-brane configuration determined by closed string data.