Interactions of Massless Higher Spin Fields From String Theory

TL;DR

This paper constructs vertex operators for massless higher spin fields in string theory, deriving their interactions and gauge symmetries, and provides a method to compute gauge-invariant cubic interactions explicitly.

Contribution

It introduces a new algorithm for calculating gauge-invariant cubic interactions of massless higher spins within string theory.

Findings

Derived vertex operators satisfying Fierz-Pauli conditions

Established gauge invariance from BRST nontriviality

Explicitly computed interactions for specific spin combinations

Abstract

We construct vertex operators for massless higher spin fields in RNS superstring theory and compute some of their three-point correlators, describing gauge-invariant cubic interactions of the massless higher spins. The Fierz-Pauli on-shell conditions for the higher spins (including tracelessness and vanishing divergence) follow from the BRST-invariance conditions for the vertex operators constructed in this paper. The gauge symmetries of the massless higher spins emerge as a result of the BRST nontriviality conditions for these operators, being equivalent to transformations with the traceless gauge parameter in the Fronsdal's approach. The gauge invariance of the interaction terms of the higher spins is therefore ensured automatically by that of the vertex operators in string theory. We develop general algorithm to compute the cubic interactions of the massless higher spins and use it to explicitly describe the gauge-invariant interaction of two $s=3$ and one $s=4$ massless particles.