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.
Highlights
JHEP02(2016)043 tantalizing possible avenue towards solving the cosmological constant problem [15]
We have argued that there does not exist a theory which might reasonably be described as a multiplet of partially massless spin-2 fields interacting in a Yang-Mills like fashion
The first comes from considering directly the gauge symmetries that such a theory might possess; we have explicitly checked that any putative deformation of the gauge symmetry which is linear in the fields only closes to form an algebra if it is abelian
Summary
A powerful tool in the search for nonlinear deformations of gauge symmetries is the closure condition (sometimes called the admissibility condition [32] in certain cases). At lowest order, where the tensors are field-independent, we require the gauge symmetry (2.3) to reduce to the free PM transformation. We have recovered in eq (2.17) the most general combination involving one power of Fλaαβ and two derivatives, and which trivially satisfies the closure condition (2.15) because the composition of two gauge transformations is zero. This gauge transformation is abelian, thereby ruling out a nonlinear PM theory of the Yang-Mills type. One might ask if the obstruction could be avoided by using tetrads or frame fields [11, 19, 36] rather than metrics since there are extra fields and Stuckelberg symmetries, but as long as a metric formulation can be recovered through gauge fixing and elimination of auxiliary fields, the arguments here apply
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