BCFW Recursion Relations and String Theory

TL;DR

The paper addresses the computation of tree-level string amplitudes by extending BCFW recursion using the BPST pomeron to study large-$z$ behavior. In a Regge-like region, string amplitudes exhibit sufficient falloff to enable a string-BCFW recursion, and the analysis reveals structural parallels with field theory, including KLT-like relations for gravitons. A key conjecture identifies an adjacent eikonal Regge (ER) regime where massless Type I string MHV amplitudes coincide with $ ext{N}=4$ SYM MHV amplitudes, supported by explicit 4- and 5-point checks and a BM-inspired argument; the work also derives an internal recursion for tachyon amplitudes, expressing higher-point tachyon amplitudes in terms of tachyon-only lower-point amplitudes with shifted kinematics. Collectively, these results provide a practical recursive framework for string amplitudes and uncover deep connections between string and field theoretic structures, with potential extensions to non-perturbative regimes and broader helicity sectors.

Abstract

We demonstrate that all tree-level string theory amplitudes can be computed using the BCFW recursion relations. Our proof utilizes the pomeron vertex operator introduced by Brower, Polchinski, Strassler, and Tan. Surprisingly, we find that in a particular large complex momentum limit, the asymptotic expansion of massless string amplitudes is identical in form to that of the corresponding field theory amplitudes. This observation makes manifest the fact that field-theoretic Yang-Mills and graviton amplitudes obey KLT-like relations. Moreover, we conjecture that in this large momentum limit certain string theory and field theory amplitudes are identical, and provide evidence for this conjecture. Additionally, we find a new recursion relation which relates tachyon amplitudes to lower-point tachyon amplitudes.