Coset construction for duals of non-relativistic CFTs

We systematically analyze backgrounds that are holographic duals to non-relativistic CFTs, by constructing them as cosets of the Schrödinger group and variants thereof. These cosets G/H are generically non-reductive and we discuss in generality how a metric on such spaces can be determined from a non-degenerate H-invariant symmetric two-form. Applying this to the d = 2 Schrödinger algebra, we reproduce the five-dimensional backgrounds proposed as duals of fermions at unitarity, and under reasonable physical assumptions, we demonstrate uniqueness of this background. The proposed gravity dual of the Lifshitz fixed-point, for which Galileian symmetry is absent, also fits into this organizational scheme and uniqueness of this background can also be shown.