KLT Factorization of Nonrelativistic String Amplitudes

Abstract

We continue our study of the Kawai-Lewellen-Tye (KLT) factorization of winding string amplitudes in [1]. 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.

Anisotropic compactification of nonrelativistic M-theory

“…Another interesting future direction would be to construct brane amplitudes in nonrelativistic M-theory, using the techniques developed in [65], which computed tree-level scattering amplitudes for n-particles involving D3-, D5-, and M5-branes using twistor-like spinor-helicity coordinates. Regarding the equivalence between nonrelativistic and DLCQ string scattering amplitudes studied in [17,66], the study of the brane amplitudes could potentially provide insights into resolving some of the long-standing ambiguities and discrepancies between Matrix theory and supergravity computation as discussed in previous works [67,68].…”

Aspects of Nonrelativistic Strings

“…It is therefore possible to evaluate string amplitudes in NR string theory by borrowing results directly from relativistic string theory 6. See[37] for generalizations of such localization theorems at one-loop to NR open strings. In this paper, KLT relations between tree-level NR string amplitudes are also studied 7.…”