No-go for Partially Massless Spin-2 Yang-Mills

TL;DR

The paper addresses whether a Yang–Mills–like interaction can exist for a multiplet of partially massless spin-2 fields on de Sitter space. It develops two independent no-go arguments: (i) a closure analysis shows any nonlinear two-derivative PM gauge deformation must be abelian, preventing a YM–type non-Abelian gauge algebra, and (ii) an AdS/dS/CFT–based test of boundary 3-point functions reveals the absence of an antisymmetric cubic vertex compatible with conformal invariance. Together, these results rule out a Yang–Mills–like partially massless spin-2 theory, though they do not exclude all possible PM interactions, leaving open the possibility of alternative higher-derivative or higher-spin–based constructions. The findings significantly constrain PM spin-2 self-interactions and suggest that if viable PM interactions exist, they will differ substantially from standard YM theories and perhaps align with higher-spin frameworks.

Abstract

There are various no-go results forbidding self-interactions for a single partially massless spin-2 field. Given the photon-like structure of the linear partially massless field, it is natural to ask whether a multiplet of such fields can interact under an internal Yang-Mills like extension of the partially massless symmetry. We give two arguments that such a partially massless Yang-Mills theory does not exist. The first is that there is no Yang-Mills like non-abelian deformation of the partially massless symmetry, and the second is that cubic vertices with the appropriate structure constants do not exist.