Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Disordered Holographic Systems I: Functional Renormalization

Allan Adams, Sho Yaida

TL;DR

This work introduces a holographic framework to study quenched electric disorder in strongly coupled CFTs by mapping disorder to disordered boundary conditions for a bulk U(1) field. It develops a holographic functional renormalization scheme to track how the disorder distribution P_V[W] runs with energy scale, and tests it by computing the disorder-averaged grand potential to leading order in the disorder strength f_{ m dis}. Using Gaussian disorder and the Harris criterion, the authors show that the disorder is relevant for d < 2+1, irrelevant for d > 2+1, and marginal at d = 2+1, with the final grand potential density given by [Ω(T)/V_{d-1}]_{ m d.a.} = c_0 N_{ m Gravity}^2 T^d + c_1 N_{ m Matter}^2 f_{ m dis} T^{2d-3} + O(f_{ m dis}^2). The analysis demonstrates precise cancellations of temperature-independent divergences between Maxwell and Einstein sectors, reinforcing the consistency of the holographic approach for disorder. Beyond perturbation theory, the work outlines potential nonperturbative phenomena, such as glassy phases or horizon percolation, motivating future exploration with nonperturbative tools like replicas in holography.

Abstract

We study quenched disorder in strongly correlated systems via holography, focusing on the thermodynamic effects of mild electric disorder. Disorder is introduced through a random potential which is assumed to self-average on macroscopic scales. Studying the flow of this distribution with energy scale leads us to develop a holographic functional renormalization scheme. We test this scheme by computing thermodynamic quantities and confirming that the Harris criterion for relevance, irrelevance or marginality of quenched disorder holds.

Disordered Holographic Systems I: Functional Renormalization

TL;DR

This work introduces a holographic framework to study quenched electric disorder in strongly coupled CFTs by mapping disorder to disordered boundary conditions for a bulk U(1) field. It develops a holographic functional renormalization scheme to track how the disorder distribution P_V[W] runs with energy scale, and tests it by computing the disorder-averaged grand potential to leading order in the disorder strength f_{ m dis}. Using Gaussian disorder and the Harris criterion, the authors show that the disorder is relevant for d < 2+1, irrelevant for d > 2+1, and marginal at d = 2+1, with the final grand potential density given by [Ω(T)/V_{d-1}]_{ m d.a.} = c_0 N_{ m Gravity}^2 T^d + c_1 N_{ m Matter}^2 f_{ m dis} T^{2d-3} + O(f_{ m dis}^2). The analysis demonstrates precise cancellations of temperature-independent divergences between Maxwell and Einstein sectors, reinforcing the consistency of the holographic approach for disorder. Beyond perturbation theory, the work outlines potential nonperturbative phenomena, such as glassy phases or horizon percolation, motivating future exploration with nonperturbative tools like replicas in holography.

Abstract

We study quenched disorder in strongly correlated systems via holography, focusing on the thermodynamic effects of mild electric disorder. Disorder is introduced through a random potential which is assumed to self-average on macroscopic scales. Studying the flow of this distribution with energy scale leads us to develop a holographic functional renormalization scheme. We test this scheme by computing thermodynamic quantities and confirming that the Harris criterion for relevance, irrelevance or marginality of quenched disorder holds.

Paper Structure

This paper contains 21 sections, 39 equations, 3 figures.

Table of Contents

  1. Imperfection
  2. A Model Holographic System with Quenched Disorder
  3. Gaussian distribution and Harris criterion
  4. Power of holography
  5. Intermezzo: Bulk Information
  6. Matter profile
  7. Maxwell dirt on pure anti-de Sitter (AdS)
  8. Maxwell dirt on hot black brane
  9. First-order backreaction
  10. Functional Flows
  11. Functional flow to first order in $f_{\rm dis}$
  12. Holographic Functional Renormalization
  13. Scheme in action to first order in $f_{\rm dis}$
  14. Thermodynamics
  15. Contribution from Maxwell
  16. ...and 6 more sections

Figures (3)

  • Figure 1: An event horizon is distorted inhomogeneously by random electric field, giving rise to a rugged black brane.
  • Figure 2: The flow of disorder can be represented by Feynman-Witten diagrams. Solid lines represent probe propagations of $U(1)$ gauge fields governed by $G_0$ in the vacuum whereas a wavy line represents a graviton propagation.
  • Figure 3: Backreaction of disorder can also be represented by Feynman-Witten diagrams.