Supersymmetric massive truncations of IIb supergravity on Sasaki-Einstein manifolds

Motivated by recent interest in applications of the AdS/CFT correspondence to condensed matter applications involving fermions, we present the supersymmetric completion of the recent massive truncations of IIB supergravity on Sasaki-Einstein manifolds. In particular, we reduce the fermionic sector of IIB supergravity to obtain five dimensional N=2 supergravity coupled to one hypermultiplet and one massive vector multiplet. The supersymmetry transformations and equations of motion are presented and analyzed. Finally, a particularly interesting truncation to N=2 supergravity coupled to a single hypermultiplet is presented which is the supersymmetric completion of the recently constructed bosonic theory dual to a 3+1 dimensional system exhibiting a superconducting phase transition.