SUSY properties of warped AdS₃

We examine supersymmetric properties of null-warped AdS₃, or alternatively Schrödinger geometries, dual to putative warped CFTs in two dimensions. We classify super Schrödinger subalgebras of the superalgebra psu(1, 1|2) psu(1, 1|2), corresponding to the superconformal algebra of the AdS₃ × S³ geometry. We comment on geometric realisations and provide a string theory description with enhanced supersymmetry in terms of intersecting D3-branes. For type IIB supergravity solutions based on T ^1,1, we consider the relationship between five-dimensional Schrödinger solutions and their three-dimensional null-warped counterparts, corresponding to R symmetry twists. Finally, we study a family of null-warped AdS₃ solutions in a setting where there is an ambiguity over the R symmetry and confirm that, for examples admitting a Kaluza-Klein (KK) reduction to three dimensions, the minimisation of a real superpotential of the three-dimensional gauged supergravity captures the central charge and R symmetry.