On the Tensionless Limit of String theory, Off - Shell Higher Spin Interaction Vertices and BCFW Recursion Relations

TL;DR

The authors develop an off-shell BRST-based framework to construct cubic (and, where possible, quartic) interactions of massless higher-spin fields on flat space by connecting to the tensionless limit of string theory. They examine BCFW recursion for HS theories, finding that pure massless HS exchanges struggle to satisfy constructibility in both field-theory and string-coupling regimes, unless extended/nonlocal degrees of freedom are incorporated. Their results imply that a consistent HS S-matrix in flat space may require a broader spectrum that includes Pomeron-like or other nonlocal objects, aligning with the notion that tensionless string theories possess richer structures than point-like HS fields alone. These insights bridge HS interactions, BRST formulations, and S-matrix methods, with potential implications for AdS/CFT and nonlocal extensions of HS dynamics.

Abstract

We construct an off-shell extension of cubic interaction vertices between massless bosonic Higher Spin fields on a flat background which can be obtained from perturbative bosonic string theory. We demonstrate how to construct higher quartic interaction vertices using a simple particular example. We examine whether BCFW recursion relations for interacting Higher Spin theories are applicable. We argue that for several interesting examples such relations should exist, but consistency of the theories might require that we supplement Higher Spin field theories with extended and possibly non-local objects.