Stringy Schrodinger truncations

Motivated by the desire to better understand finite-temperature holography for three-dimensional Schrodinger spacetimes, we: i) construct a four-parameter family of warped black string solutions of type IIB supergravity and ii) find the first consistent truncations of type IIB string theory to three dimensions that admit both supersymmetric Schrodinger solutions and warped generalizations of the BTZ black hole. Our analysis reveals a number of interesting features. One is that the thermodynamic properties of all the warped black strings, as well as the asymptotic symmetry group data, are identical to those of BTZ, in an appropriate parametrization. A more striking feature is that the spectrum of linearized perturbations around the various supersymmetric Schrodinger vacua oftentimes contains modes that carry energy flux through the spacetime boundary, which are usually believed to be unstable. A preliminary analysis indicates that, at least in the case of most interest, these modes do not lead to an instability.