Non-relativistic holography

TL;DR

This work develops holographic duals for d-dimensional, scale-invariant but non-Lorentz invariant field theories that do not possess full Schrödinger symmetry. It constructs $(d+1)$-dimensional gravity backgrounds using diverse matter sectors (notably massive vector fields and scalar–gauge systems) and provides finite-temperature black-brane generalizations whose thermodynamics align with anisotropic scaling expectations. The paper also explores string/brane embeddings and interprets these geometries as marginal, non-Lorentz invariant deformations of CFTs, while initiating holographic renormalization to obtain well-defined correlation functions. Together, these advances establish a framework for studying non-relativistic, anisotropic critical points, including their finite-temperature behavior and correlation structure, and lay groundwork for transport and phase structure analyses in such theories.

Abstract

We consider holography for d-dimensional scale invariant but non-Lorentz invariant field theories, which do not admit the full Schrodinger symmetry group. We find new realizations of the corresponding (d+1)-dimensional gravity duals, engineered with a variety of matter Lagrangians, and their finite temperature generalizations. The thermodynamic properties of the finite temperature backgrounds are precisely those expected for anisotropic, scale invariant field theories. The brane and string theory realizations of such backgrounds are briefly discussed, along with their holographic interpretation in terms of marginal but non Lorentz invariant deformations of conformal field theories. We initiate discussion of holographic renormalization in these backgrounds, and note that such systematic renormalization is necessary to obtain the correct behavior of correlation functions.