Cubic interactions for massless and partially massless spin-1 and spin-2 fields

TL;DR

This paper classifies all consistent two-derivative cubic couplings among massless and partially massless spin-1 and spin-2 fields in (A)dS space, revealing a unique mixing candidate and conditions for consistent theories.

Contribution

It provides a complete classification of cubic interactions, including a new mixing between spin-1 and PM spin-2 fields, and derives constraints on structure constants allowing for various kinetic term signs.

Findings

Identifies a unique spin-1 and PM spin-2 mixing candidate.

Derives quadratic constraints on structure constants.

Shows that consistent theories with no relative signs are multiple conformal gravity copies coupled to Yang-Mills in D=4.

Abstract

We perform a complete classification of the consistent two-derivative cubic couplings for a system containing an arbitrary number of massless spin-1, massless spin-2, and partially massless (PM) spin-2 fields in $D$-dimensional (anti-)de Sitter space. In addition to previously known results, we find a unique candidate mixing between spin-1 and PM spin-2 fields. We derive all the quadratic constraints on the structure constants of the theory, allowing for relative ``wrong-sign'' kinetic terms for any of the fields. In the particular case when the kinetic terms in each sector have no relative signs, we find that the unique consistent non-trivial theory is given by multiple independent copies of conformal gravity coupled to a Yang-Mills sector in $D=4$. Our results strengthen the well-known no-go theorems on the absence of mutual interactions for massless and PM spin-2 fields.