Holographic two-point functions in a disorder system

TL;DR

This paper explores the holographic duality of two-point functions in nonconformal field theories, focusing on Lifshitz geometries and disorder-induced RG flows, revealing how operator dimensions evolve along the flow.

Contribution

It explicitly demonstrates the holographic relation between Lifshitz geometries and Lifshitz field theories, including the effects of disorder deformations on operator dimensions.

Findings

Calculated two-point correlators in Lifshitz geometries.

Showed the flow from UV conformal to IR Lifshitz theories.

Analyzed anomalous dimensions during RG flow.

Abstract

We study the holographic dual of two-point correlation functions for nonconformal field theories. We first take into account a Lifshitz geometry as the dual of a Lifshitz field theory which may appear at a critical or IR fixed point. We explicitly show the holographic relation between a Lifshitz geometry and a Lifshitz field theory by calculating two-point correlators and equation of state parameter on both sides. We also investigate a disorder deformation, which allows a UV conformal field theory to flow into a new IR Lifshitz field theory. In this deformed theory, we investigate an anomalous dimension representing the change of an operator's scaling dimension along the RG flow.