Hyperscaling violating Lifshitz holography

TL;DR

This paper develops a comprehensive holographic dictionary for Lifshitz and hyperscaling violating Lifshitz backgrounds with arbitrary exponents, enabling better understanding of dual non-relativistic field theories.

Contribution

It provides a systematic method to construct the holographic dictionary for these backgrounds within a generic Einstein-Proca-Dilaton framework, including asymptotic expansions and Ward identities.

Findings

Constructed the holographic dictionary for Lifshitz backgrounds.

Derived Fefferman-Graham asymptotic expansions.

Established non-relativistic holographic Ward identities.

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.