Something to do with Schrödinger spacetimes

Abstract

We present a brief review of the AdS/CFT correspondence and the progress made toward building a realistic gravity/gauge theory duality for a non-relativistic conformal field theory. In particular, we highlight many of the computational tools necessary for such a program before introducing one such model duality. The model presented exhibits the symmetry group of Schrodinger's equation along with conformal symmetry. A black hole can be placed in this spacetime to study a finite temperature duality. In the low-frequency, long-distance limit at finite temperature classical hydrodynamics can be used to determine the retarded Green's functions of the field theory, which can be computed from the gravity dual. This facilitates the calculation of several characteristic quantities including the shear viscosity and the shear diffusion constant giving results consistent with other hydrodynamic analyses of the system.