KLT Factorization of Nonrelativistic String Amplitudes

Abstract

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.

37 pages, minor clarifications in v2

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• Worldsheet Formalism for Decoupling Limits in String Theory
• The Supersymmetric Neveu-Schwarz Branes of Non-Relativistic String Theory
• Matrix Theory Reloaded: A BPS Road to Holography
• Non-Lorentzian IIB Supergravity from a Polynomial Realization of SL(2,R)
• Anisotropic Compactification of Nonrelativistic M-Theory
• Branched SL(2,Z) Duality
• Nonrelativistic expansion of M2 branes and M theory backgrounds