  We continue our study of the Kawai-Lewellen-Tye (KLT) factorization of
winding string amplitudes. In a toroidal compactification, amplitudes for
winding closed string states factorize into products of amplitudes for open
strings ending on an array of D-branes localized in the compactified
directions; the specific D-brane configuration is determined by the closed
string data. In this paper, we study a zero Regge slope limit of the KLT
relations between winding string amplitudes. Such a limit of string theory
requires a critically tuned Kalb-Ramond field in a compact direction, and leads
to a self-contained corner called nonrelativistic string theory. This theory is
unitary, ultraviolet complete, and its string spectrum and spacetime S-matrix
satisfy nonrelativistic symmetry. Moreover, the asymptotic closed string states
in nonrelativistic string theory necessarily carry nonzero windings. First,
starting with relativistic string theory, we construct a KLT factorization of
amplitudes for winding closed strings in the presence of a critical Kalb-Ramond
field. Then, in the zero Regge limit, we uncover a KLT relation for amplitudes
in nonrelativistic string theory. Finally, we show how such a relation can be
reproduced from first principles in a purely nonrelativistic string theory
setting. We will also discuss connections to the amplitudes of string theory in
the discrete light cone quantization (DLCQ), a method that is relevant for
Matrix theory.
