We analyze quartic gauge-invariant interactions of massless higher spin fields by using vertex operators constructed in our previous works and computing their 4-point amplitudes in superstring theory. The kinematic part of the quartic interactions of the higher spins is determined by the matter structure of their vertex operators; the nonlocality of the interactions is the consequence of the specific ghost structure of these operators. We compute explicitly the 4-point amplitude describing the complete gauge-invariant 1 À 1 À 3 À 3 quartic interaction (two massless spin 3 particles interacting with two photons) and comment on more general 1 À 1 À s À s cases, particularly pointing out the structure of 1 À 1 À 5 À 5 coupling.

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.October 2009 † dimitri.polyakov@wits.ac.za

We calculate the interaction 3-vertex of two massless spin 3 particles with a graviton using vertex operators for spin 3 fields in open string theory, constructed in our previous work. The massless spin 3 fields are shown to interact with the graviton through the linearized Weyl tensor, reproducing the result by Boulanger, Leclercq and Sundell. This is consistent with the general structure of the non-Abelian 2 − s − s couplings, implying that the minimal number of space-time derivatives in the interaction vertices of two spin s and one spin 2 particle is equal to 2s − 2.May 2010 † dimitri.polyakov@wits.ac.za