Abstract
We find and classify the simplest mathcal{N} = 2 SUSY multiplets on AdS4 which contain partially massless fields. We do this by studying representations of the mathcal{N} = 2, d = 3 superconformal algebra of the boundary, including new shortening conditions that arise in the non-unitary regime. Unlike the mathcal{N} = 1 case, the simplest mathcal{N} = 2 multiplet containing a partially massless spin-2 is short, containing several exotic fields. More generally, we argue that mathcal{N} = 2 supersymmetry allows for short multiplets that contain partially massless spin-s particles of depth t = s − 2.
Highlights
T = s − 1 field corresponds to the usual massless representation
We argue that N = 2 supersymmetry allows for short multiplets that contain partially massless spin-s particles of depth t = s − 2
From the boundary conformal field theory (CFT) point of view, PM fields in AdS are dual to CFT currents satisfying higher derivative conservation conditions [44], which occur only in non-unitary CFTs
Summary
As in [12], we study supersymmetric extensions of the PM representations via the AdS/CFT correspondence. We are interested in AdS4 SUSY, we study d = 3 superconformal symmetry on the boundary. P i, J ij , D, Ki, QaI , SaI , RIJ. The SaI are the special superconformal generators, and the anti-symmetric RIJ are so(N ) R-symmetries, which together complete the SUSY generators and conformal generators into to the N extended superconformal algebra. P j = 2(δijD + iJ ij) , J ij , Kk = i −δkiKj + δkjKi. The commutators which when taken together with (2.2) form the N extended SUSY algebra are. The first line (2.4) is the main anti-commutator indicative of SUSY, (2.5) shows that QaI transforms as a spinor under rotations, (2.6) is the statement that RIJ forms an so(N ), and (2.7) shows that QaI transforms as a vector under this so(N ). The (anti)commutation relations above are all consistent with the reality conditions (2.9)
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