Fermions and the Sch/nrCFT Correspondence

We consider the problem of Dirac fermions propagating on a spacetime of Schr\"odinger isometry and the associated boundary Euclidean two-point function of fermionic scaling operators of the holographic dual non-relativistic conformal theory. Paying careful attention to the representations of the Schr\"odinger algebra that appear in this problem, we show carefully how the on-shell action is constructed and how the boundary theory may be renormalized consistently by the inclusion of appropriate Galilean invariant boundary counterterms.