Non-relativistic holography

TL;DR

This paper explores holographic duals for non-Lorentz invariant, scale-invariant field theories, presenting new gravity solutions, analyzing their thermodynamics, and discussing their string theory realizations and holographic renormalization.

Contribution

It introduces new gravity duals for non-Lorentz invariant theories, including finite temperature solutions and holographic renormalization methods.

Findings

Thermodynamics matches expectations for anisotropic, scale-invariant theories.

New gravity solutions constructed with various matter Lagrangians.

Holographic renormalization is essential for correct correlation functions.

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.