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

TL;DR

The paper proves that a Yang-Mills extension for partially massless spin-2 fields cannot exist due to the absence of necessary non-abelian deformations and cubic interaction vertices.

Contribution

It provides two rigorous arguments demonstrating the non-existence of partially massless Yang-Mills theories, extending no-go results for self-interactions of such fields.

Findings

No Yang-Mills like non-abelian deformation exists.

Cubic vertices with appropriate structure constants do not exist.

Partially massless spin-2 fields cannot form interacting Yang-Mills theories.

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.