Fermions and type IIB supergravity on squashed Sasaki-Einstein manifolds

We discuss the dimensional reduction of fermionic modes in a recently found class of consistent truncations of type IIB supergravity compactified on squashed fivedimensional Sasaki-Einstein manifolds. We derive the lower dimensional equations of motion and effective action, and comment on the supersymmetry of the resulting theory, which is consistent with N = 4 gauged supergravity in d = 5, coupled to two vector multiplets. We compute fermion masses by linearizing around two AdS₅ vacua of the theory: one that breaks N = 4 down to N = 2 spontaneously, and a second one which preserves no supersymmetries. The truncations under consideration are noteworthy in that they retain massive modes which are charged under the U(1) R-symmetry, a feature that makes them interesting for applications to condensed matter phenomena via gauge/gravity duality. In this light, as an application of our general results we exhibit the coupling of the fermions to the type IIB holographic superconductor, and find a consistent further truncation of the fermion sector that retains a single spin-1/2 mode.