Lifshitz as a deformation of Anti-de Sitter

TL;DR

This paper explores how small deformations of relativistic conformal field theories lead to Lifshitz scaling, using holography and Einstein-Proca models to analyze the dual field theories and their invariance properties.

Contribution

It establishes a holographic framework for Lifshitz spacetimes with small dynamical exponent deviations and connects these to specific deformations of CFTs.

Findings

Holographic dictionary constructed up to order epsilon^2

Two-point function verified to be Lifshitz invariant

Deformations of CFTs can generically produce Lifshitz scaling

Abstract

We consider holography for Lifshitz spacetimes with dynamical exponent z=1+epsilon^2, where epsilon is small. We show that the holographically dual field theory is a specific deformation of the relativistic CFT, corresponding to the z=1 theory. Treating epsilon as a small expansion parameter we set up the holographic dictionary for Einstein-Proca models up to order epsilon^2 in three and four bulk dimensions. We explain how renormalization turns the relativistic conformal invariance into non-relativistic Lifshitz invariance with dynamical exponent z=1+epsilon^2. We compute the two-point function of the conserved spin two current for the dual two-dimensional field theory and verify that it is Lifshitz invariant. Using only QFT arguments, we show that a particular class of deformations of CFTs generically leads to Lifshitz scaling invariance and we construct examples of such deformations.