Gravitational Couplings of Higher Spins from String Theory

Understand

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 $2s-2$.