KLT Factorization of Winding String Amplitudes

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.

Scattering Amplitudes of Kaluza-Klein Strings and Extended Massive Double-Copy

“…and make the rescaling (α , R, L) → 1 4 (α , R, L), such that the mass spectrum (2.10) of open strings coincides with the mass spectrum (2.4) of closed strings [23].…”

“…The essential advantage of the compactified KK string theory is that the connection between the KK closed-string amplitudes and the proper products of KK open-string amplitudes can be intrinsically built in from the start. A recent literature [23] studied the KLT factorization of winding string amplitudes of tachyons in the bosonic string theory, but did not consider the amplitudes of KK open and closed strings. We will study the scattering amplitudes of massive KK states of open and closed bosonic strings, and derive the corresponding scattering amplitudes of KK gauge-bosons and of KK gravitons in the low energy field-theory limit.…”