Disorder in AdS$_3$/CFT$_2$

TL;DR

This paper investigates the effects of marginally relevant quenched disorder in AdS$_3$/CFT$_2$ using a perturbative approach, revealing unphysical features from disorder averaging and proposing a resummation method to address them.

Contribution

It introduces a perturbative framework for disorder in AdS$_3$/CFT$_2$ and develops a resummation technique to eliminate unphysical artifacts from disorder averaging.

Findings

Disorder induces a small mass and angular momentum in the bulk.

Unphysical features arise from disorder averaging.

A Poincaré-Lindstedt-inspired resummation removes these features.

Abstract

We perturbatively study marginally relevant quenched disorder in AdS$_3$/CFT$_2$ to second order in the disorder strength. Using the Chern-Simons formulation of AdS$_3$ gravity for the Poincar\'e patch, we introduce disorder via the chemical potentials. We discuss the bulk and boundary properties resulting from the disorder averaged metric. The disorder generates a small mass and angular momentum. In the bulk and the boundary, we find unphysical features due to the disorder average. Motivated by these features, we propose a Poincar\'e-Lindstedt-inspired resummation method. We discuss how this method enables us to remove all of the unphysical features and compare with other approaches to averaging.