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 $\theta$, compatible with the null energy condition, which was recently developed in [1,2]. 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.

7 pages. Based on talks given at ICHEP 2014 and the "Quantum Field Theory, String Theory and Condensed Matter Physics" conference in Kolymbari, Crete. To appear in the proceedings of ICHEP 2014

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