Deformations of Lifshitz Holography in $(n+1)$-dimensions

TL;DR

This paper explores how Lifshitz holography deforms in higher dimensions, focusing on marginally relevant operators at a specific dynamical critical exponent, and analyzes the resulting RG flow from Lifshitz to AdS geometries.

Contribution

It provides a detailed study of deformations at $z=n-1$, deriving RG flows and physical quantities in the quantum critical regime within higher-dimensional Lifshitz holography.

Findings

RG flow from Lifshitz to AdS geometries at finite temperature

Dependence of free energy and energy densities on $ extlog(rac{ extLambda^z}{T})$

Characterization of marginally relevant operators at $z=n-1$

Abstract

We investigate deformations of Lifshitz holography in $(n+1)$ dimensional spacetime. After discussing the situation for general Lifshitz scaling symmetry parameter $z$, we consider $z=n-1$ and the associated marginally relevant operators. These operators are dynamically generated by a momentum scale $\Lambda \sim 0$ and correspond to slightly deformed Lifshitz spacetimes via a holographic picture. We obtain renormalization group flow at finite temperature from UV Lifshitz to IR AdS, and evaluate how physical quantities such as the free energy density and the energy density depend on $\log(\Lambda^z/T)$ in the quantum critical regime as $\Lambda^z/T \rightarrow 0$.