  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.
