Interactions of partially massless spin-2 with spin-3/2 fields are obstructed at second order unless a massless graviton is added, leading to N=1 conformal supergravity.
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A note on partially massless supergravity
Interactions of partially massless spin-2 with spin-3/2 fields are obstructed at second order unless a massless graviton is added, leading to N=1 conformal supergravity.