Interacting Higher Spins and the High Energy Limit of the Bosonic String

TL;DR

The paper investigates the high-energy (tensionless) limit of the bosonic open string to construct an exact, BRST-invariant cubic vertex for interactions of an infinite tower of massless higher-spin fields in flat space. Using an OSFT-inspired BRST framework, it demonstrates that the gauge algebra closes to all orders without requiring quartic or higher-order terms and provides explicit vertex structures for both totally symmetric and mixed-symmetry fields. The work extends the construction to AdS, finding that a naive AdS deformation does not exist within their ansatz, and discusses implications for connections between higher-spin gauge theories and string theory, potentially in AdS/CFT contexts. Overall, it delivers a concrete, off-shell HS interaction vertex with exact gauge invariance rooted in the high-energy limit of string theory, highlighting the role of an infinite HS tower for consistency.

Abstract

In this note, we construct a BRST invariant cubic vertex for massless fields of arbitrary mixed symmetry in flat space-time. The construction is based on the vertex given in bosonic Open String Field Theory. The algebra of gauge transformations is closed without any additional, higher than cubic, couplings due to the presence of an infinite tower of massless fields. We briefly discuss the generalization of this result to a curved space-time and other possible implications.