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Register a new userDual actions for massless, partially-massless and massive gravitons in (A)dS
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We provide a unified treatment of electric-magnetic duality, at the action level and with manifest Lorentz invariance, for massive, massless as well as partially-massless gravitons propagating in maximally symmetric spacetimes of any dimension n>3. For massive and massless fields, we complete previous analyses that use parent-action techniques by giving dual descriptions that enable direct counting of physical degrees of freedom in the flat and massless limit. The same treatment is extended to the partially-massless case, where the duality has been previously discussed in covariant form only at the level of the equations of motion. The nature of the dual graviton is therefore clarified for all values of the mass and of the cosmological constant.
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We determine the current exchange amplitudes for free totally symmetric tensor fields $vf_{mu_1 ... mu_s}$ of mass $M$ in a $d$-dimensional $dS$ space, extending the results previously obtained for $s=2$ by other authors. Our construction is based on an unconstrained formulation where both the higher-spin gauge fields and the corresponding gauge parameters $Lambda_{mu_1 >... mu_{s-1}}$ are not subject to Fronsdals trace constraints, but compensator fields $alpha_{mu_1 ... mu_{s-3}}$ are introduced for $s > 2$. The free massive $dS$ equations can be fully determined by a radial dimensional reduction from a $(d+1)$-dimensional Minkowski space time, and lead for all spins to relatively handy closed-form expressions for the exchange amplitudes, where the external currents are conserved, both in $d$ and in $(d+1)$ dimensions, but are otherwise arbitrary. As for $s=2$, these amplitudes are rational functions of $(ML)^2$, where $L$ is the $dS$ radius. In general they are related to the hypergeometric functions $_3F_2(a,b,c;d,e;z)$, and their poles identify a subset of the partially-massless discrete states, selected by the condition that the gauge transformations of the corresponding fields contain some non-derivative terms. Corresponding results for $AdS$ spaces can be obtained from these by a formal analytic continuation, while the massless limit is smooth, with no van Dam-Veltman-Zakharov discontinuity.
We study the possibility for a unitary theory of partially-massless (PM) spin-two field interacting with Gravity in arbitrary dimensions. We show that the gauge and parity invariant interaction of PM spin two particles requires the inclusion of specific massive spin-two fields and leads to a reconstruction of Conformal Gravity, or multiple copies of the latter in even dimensions. By relaxing the parity invariance, we find a possibility of a unitary theory in four dimensions, but this theory cannot be constructed in the standard formulation, due to the absence of the parity-odd cubic vertex therein. Finally, by relaxing the general covariance, we show that a `non-geometric coupling between massless and PM spin-two fields may lead to an alternative possibility of a unitary theory. We also clarify some aspects of interactions between massless, partially-massless and massive fields, and resolve disagreements in the literature.
We study a class of non-unitary so(2,d) representations (for even values of d), describing mixed-symmetry partially massless fields which constitute natural candidates for defining higher-spin singletons of higher order. It is shown that this class of so(2,d) modules obeys of natural generalisation of a couple of defining properties of unitary higher-spin singletons. In particular, we find out that upon restriction to the subalgebra so(2,d-1), these representations branch onto a sum of modules describing partially massless fields of various depths. Finally, their tensor product is worked out in the particular case of d=4, where the appearance of a variety of mixed-symmetry partially massless fields in this decomposition is observed.
We revisit the problem of building consistent interactions for a multiplet of partially massless spin-2 fields in (anti-)de Sitter space. After rederiving and strengthening the existing no-go result on the impossibility of Yang-Mills type non-abelian deformations of the partially massless gauge algebra, we prove the uniqueness of the cubic interaction vertex and field-dependent gauge transformation that generalize the structures known from single-field analyses and in four spacetime dimensions, where our results also hold. Unlike in the case of one partially massless field, however, we show that for two or more particle species the cubic deformations can be made consistent at the complete non-linear level, albeit at the expense of allowing for negative relative signs between kinetic terms, making our new theory akin to conformal gravity. Our construction thus provides the first example of an interacting theory containing only partially massless fields.
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.
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