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Register a new userSupersymmetric Partially Massless Fields and Non-Unitary Superconformal Representations
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We find and classify the ${cal N}=1$ SUSY multiplets on AdS$_4$ which contain partially massless fields. We do this by studying the non-unitary representations of the $d=3$ superconformal algebra of the boundary. The simplest super-multiplet which contains a partially massless spin-2 particle also contains a massless photon, a massless spin-$3/2$ particle and a massive spin-$3/2$ particle. The gauge parameters form a Wess-Zumino super-multiplet which contains the gauge parameters of the photon, the partially massless graviton, and the massless spin-$3/2$ particle. We find the AdS$_4$ action and SUSY transformations for this multiplet. More generally, we classify new types of shortening conditions that can arise for non-unitary representations of the $d=3$ superconformal algebra.
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We find and classify the simplest ${cal N}=2$ SUSY multiplets on AdS$_4$ which contain partially massless fields. We do this by studying representations of the ${cal N}=2$, $d=3$ superconformal algebra of the boundary, including new shortening conditions that arise in the non-unitary regime. Unlike the ${cal N}=1$ case, the simplest ${cal N}=2$ multiplet containing a partially massless spin-2 is short, containing several exotic fields. More generally, we argue that ${cal N}=2$ supersymmetry allows for short multiplets that contain partially massless spin-$s$ particles of depth $t=s-2$.
We provide a systematic and comprehensive derivation of the linearized dynamics of massive and partially massless spin-2 particles in a Schwarzschild (anti) de Sitter black hole background, in four and higher spacetime dimensions. In particular, we show how to obtain the quadratic actions for the propagating modes and recast the resulting equations of motion in a Schrodinger-like form. In the case of partially massless fields in Schwarzschild de Sitter spacetime, we study the isospectrality between modes of different parity. In particular, we prove isospectrality analytically for modes with multipole number $L=1$ in four spacetime dimensions, providing the explicit form of the underlying symmetry. We show that isospectrality between partially massless modes of different parity is broken in higher-dimensional Schwarzschild de Sitter spacetimes.
We construct a non-linear theory of interacting spin-2 fields that is invariant under the partially massless (PM) symmetry to all orders. This theory is based on the SO(1,5) group, in analogy with the SO(2,4) formulation of conformal gravity, but has a quadratic spectrum free of ghost instabilities. The action contains a vector field associated to a local SO(2) symmetry which is manifest in the vielbein formulation of the theory. We show that, in a perturbative expansion, the SO(2) symmetry transmutes into the PM transformations of a massive spin-2 field. In this context, the vector field is crucial to circumvent earlier obstructions to an order-by-order construction of PM symmetry. Although the non-linear theory lacks enough first class constraints to remove all helicity-0 modes from the spectrum, the PM transformations survive to all orders. The absence of ghosts and strong coupling effects at the non-linear level are not addressed here.
In this paper we investigate a particular ghost-free bimetric theory that exhibits the partially massless (PM) symmetry at quadratic order. At this order the global SO(1,4) symmetry of the theory is enhanced to SO(1,5). We show that this global symmetry becomes inconsistent at cubic order, in agreement with a previous calculation. Furthermore, we find that the PM symmetry of this theory cannot be extended beyond cubic order in the PM field. More importantly, it is shown that the PM symmetry cannot be extended to quartic order in any theory with one massless and one massive spin-2 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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