Disordered Systems and the Replica Method in AdS/CFT

TL;DR

This paper develops a holographic approach using the replica method to analyze disorder effects in conformal field theories within the AdS/CFT framework, revealing significant changes in correlation functions and RG flow due to disorder.

Contribution

It introduces a holographic replica method to incorporate disorder in CFTs and explores its impact on correlation functions and RG flow.

Findings

Disorder can drastically alter the scaling of two-point functions.

The holographic replica method effectively models Gaussian disorder in CFTs.

Disorder influences the renormalization group flow of the effective central charge.

Abstract

We formulate a holographic description of effects of disorder in conformal field theories based on the replica method and the AdS/CFT correspondence. Starting with $n$ copies of conformal field theories, randomness with a gaussian distribution is described by a deformation of double trace operators. After computing physical quantities, we take the $n \to 0$ limit at the final step. We compute correlation functions in the disordered systems by using the holographic replica method as well as the formulation in the conformal field theory. We find examples where disorder changes drastically the scaling of two point functions. The renormalization group flow of the effective central charge in our disordered systems is also discussed.