Interactions of Massless Higher Spin Fields From String Theory

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.