SUSY properties of warped AdS$_3$

We examine supersymmetric properties of null-warped AdS$_3$, or alternatively Schrodinger geometries, dual to putative warped CFTs in two dimensions. We classify super Schrodinger subalgebras of the superalgebra psu(1, 1$|$2) $\oplus$ psu(1, 1$|$2), corresponding to the superconformal algebra of the AdS$_3 \times$ S$^3$ 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 Schrodinger solutions and their three-dimensional null-warped counterparts, corresponding to R symmetry twists. Finally, we study a family of null-warped AdS$_3$ 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.

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