  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.
