Gravitational Couplings of Higher Spins from String Theory

TL;DR

This paper computes the interaction vertex between two massless spin 3 particles and a graviton in string theory, revealing the interaction structure and derivative count consistent with higher-spin theories.

Contribution

It constructs explicit vertex operators for spin 3 fields in string theory and derives their interaction with gravitons, confirming theoretical predictions about derivative order in higher-spin couplings.

Findings

Interaction via linearized Weyl tensor matches previous results.

Minimal derivatives in 2-s-s couplings are 2s-2.

String theory provides explicit vertices for higher-spin interactions.

Abstract

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 $2s-2$.