Lifshitz holography

TL;DR

This article surveys Lifshitz holography, detailing the gravity duals that realize non relativistic scaling, the construction of bottom up and top down models, and the subtleties of holographic renormalization and the holographic dictionary. It analyzes correlation functions, hydrodynamics, and anomalies, and discusses extensions to HV geometries and Newton–Cartan structures. The work highlights that Lifshitz symmetry alone does not fix correlators, emphasizes the central role of the energy momentum complex, and outlines how entanglement, NC geometry, and running scalars shape the dual field theories. It also surveys applications to condensed matter and the challenges in top down embeddings and real time holography, pointing to key open questions for future research.

Abstract

In this article we review recent progress on the holographic modelling of field theories with Lifshitz symmetry. We focus in particular on the holographic dictionary for Lifshitz backgrounds - the relationship between bulk fields and boundary operators, operator correlation functions and underlying geometrical structure. The holographic dictionary is essential in identifying the universality class of strongly coupled Lifshitz theories described by gravitational models.