Partially massless spin 2 and supersymmetry

Abstract: The very existence of partially massless spin 2 supermultiplet tell us that partially massless spin 2 has two natural superpartners: massless spin 3/2 and massive spin 3/2 with some special value of mass. As for any pair of fields connected by global supertransformations there are two natural questions: existence of the self-interaction and possibility to make supertransformations to be local by switching their interaction with massless spin 3/2 gravitino. At first, we consider a self-interaction for the partially massless spin 2 and massive spin 3/2 which may be considered as the first approximation to partially massless supergravity and provide a direct construction of the minimal (i.e. having no more than one derivative) vertex which resembles usual supergravity. Then we consider localization of global supersymmetry which connects partially massless spin 2 with its two possible superpartners -- massless spin 3/2 and massive with special mass value. For the first case we also managed to construct a minimal vertex having no more that one derivative. Again this vertex can be considered as a part of what can be called partially massless $N=2$ supergravity. As for the second case, the corresponding vertex does exist but it has higher derivative terms.