Abstract
We find and classify the mathcal{N}=1 SUSY multiplets on AdS4 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 AdS4 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.
Highlights
From the particle, leaving a number of degrees of freedom intermediate between that of a massless and a massive field
We classify new types of shortening conditions that can arise for non-unitary representations of the d = 3 superconformal algebra
(This is the normal quantization root ∆+, the alternate root is ∆− = 1 − t.) The partially massless fields are dual to short multiplets with tensor spinor conformal primaries |∆ i1···is−1/2 a that have a null descendent at level s − t, Pi1 . . . Pis−t |∆ i1···is−1/2 a = 0
Summary
Through the AdS/CFT correspondence, a spin s field in AdS4 corresponds to a spin s primary operator in CFT3. The mass m of the field and the dimension ∆ of the primary are related by m2L2 = ∆(∆ − 3), s = 0,. There are two different ways to quantize the field in AdS4. These correspond to the greater and lesser roots of (2.1), ∆±. ∆+ corresponds to the so-called “standard quantization” which covers the operators with ∆ > 3/2, and ∆− to the “alternate quantization” [59] which covers the operators with ∆ < 3/2. Theories containing primary operators violating these bounds are necessarily non-unitary
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