Partially Massless Spin 2 Electrodynamics
S. Deser, A. Waldron
TL;DR
The paper investigates whether maximal-depth partially massless spin-2 excitations in de Sitter space can mediate charged matter interactions, motivated by their lightlike propagation and conformal invariance. By recasting the PM spin-2 field into a Maxwell-like curvature and coupling to a conserved vector current via a derivative interaction, it derives the one-particle exchange amplitude ${\cal A}_{\rm pp}=\frac{Q^2}{2}\int J (\square+6) J$ and shows that the total amplitude including the usual Maxwell exchange is ${\cal A}_{\rm tot}=\int J \frac{e^2}{\square}\left[1+\frac{q^2}{2e^2}\frac{3\square}{\Lambda}\left(\frac{3\square}{\Lambda}+6\right)\right] J$, with $q^2=\frac{Q^2\Lambda}{3}$. It concludes that the partial photon cannot replace the standard photon but can modify short-range electromagnetic interactions, and analyzes higher-derivative counterterms, which can alter the amplitude but may introduce ghosts; the work assumes a fixed de Sitter background and points to the need for coupling to gravity for a full treatment.
Abstract
We propose that maximal depth, partially massless, higher spin excitations can mediate charged matter interactions in a de Sitter universe. The proposal is motivated by similarities between these theories and their traditional Maxwell counterpart: their propagation is lightlike and corresponds to the same Laplacian eigenmodes as the de Sitter photon; they are conformal in four dimensions; their gauge invariance has a single scalar parameter and actions can be expressed as squares of single derivative curvature tensors. We examine this proposal in detail for its simplest spin 2 example. We find that it is possible to construct a natural and consistent interaction scheme to conserved vector electromagnetic currents primarily coupled to the helicity 1 partially massless modes. The resulting current-current single ``partial-photon'' exchange amplitude is the (very unCoulombic) sum of contact and shorter-range terms, so the partial photon cannot replace the traditional one, but rather modifies short range electromagnetic interactions. We also write the gauge invariant fourth-derivative effective actions that might appear as effective corrections to the model, and their contributions to the tree amplitude are also obtained.