Towards a Non-Relativistic Holographic Superfluid

We explore the phase structure of a holographic toy model of superfluid states in non-relativistic conformal field theories. At low background mass density, we find a familiar second-order transition to a superfluid phase at finite temperature. Increasing the chemical potential for the probe charge density drives this transition strongly first order as the low-temperature superfluid phase merges with a thermodynamically disfavored high-temperature condensed phase. At high background mass density, the system reenters the normal phase as the temperature is lowered further, hinting at a zero-temperature quantum phase transition as the background density is varied. Given the unusual thermodynamics of the background black hole, however, it seems likely that the true ground state is another configuration altogether.Comment: 13+5 pages, late

Classical Integrability of the Squashed Three-sphere, Warped AdS3 and Schroedinger Spacetime via T-Duality

We discuss the integrability of 2d non-linear sigma models with target space being the squashed three-sphere, warped anti-de Sitter space and the Schroedinger spacetime. These models can be obtained via T-duality from integrable models. We construct an infinite family of non-local conserved charges from the T-dual Lax currents, enhancing the symmetry of warped anti-de Sitter space and the Schroedinger spacetime to sl2(R)+sl2(R).Comment: 29 Pages, 3 appendices. Minor changes: added references, footnot

Holography for Schrodinger backgrounds

We discuss holography for Schrodinger solutions of both topologically massivegravity in three dimensions and massive vector theories in (d+1) dimensions. Inboth cases the dual field theory can be viewed as a d-dimensional conformalfield theory (two dimensional in the case of TMG) deformed by certain operatorsthat respect the Schrodinger symmetry. These operators are irrelevant from theviewpoint of the relativistic conformal group but they are exactly marginalwith respect to the non-relativistic conformal group. The spectrum of linearfluctuations around the background solutions corresponds to operators that arelabeled by their scaling dimension and the lightcone momentum k_v. We set upthe holographic dictionary and compute 2-point functions of these operatorsboth holographically and in field theory using conformal perturbation theoryand find agreement. The counterterms needed for holographic renormalization arenon-local in the v lightcone direction.<br/