Hyperscaling violating Lifshitz holography

Abstract

We present an overview of the construction of the general holographic dictionary for asymptotically locally Lifshitz and hyperscaling violating Lifshitz backgrounds with arbitrary dynamical exponents z and θ, compatible with the null energy condition, which was recently developed in [W. Chemissany, I. Papadimitriou, Generalized dilatation operator method for non-relativistic holography, arXiv:1405.3965, W. Chemissany, I. Papadimitriou, Lifshitz holography: The whole shebang, arXiv:1408.0795]. A concrete definition of asymptotically locally Lifshitz and hyperscaling violating Lifshitz backgrounds is provided in the context of a generic bottom-up Einstein-Proca-Dilaton theory, and a systematic procedure for solving the radial Hamilton-Jacobi equation via a covariant expansion in eigenfunctions of two commuting operators is presented. The resulting asymptotic solution of the Hamilton-Jacobi equation is subsequently used to derive the full holographic dictionary, including the Fefferman-Graham asymptotic expansions and the non-relativistic holographic Ward identities.