# Metal or Insulator? Dirac operator spectrum in holographic QCD

## TL;DR

This paper explores the localization properties of Dirac operator eigenmodes in QCD using holographic models, linking confinement phases to delocalization and deconfinement to localization phenomena.

## Contribution

It provides a holographic explanation for the localization behavior of Dirac eigenmodes in QCD, connecting confinement phases to delocalization and deconfinement to localization.

## Key findings

- Delocalization in confined phase linked to $ heta=\pi$ phenomena.
- Localized modes in deconfined phase associated with near-horizon holographic regions.
- Holographic perspective offers a conjectural explanation for lattice QCD observations.

## Abstract

The lattice studies in QCD demonstrate the nontrivial localization behavior of the eigenmodes of the 4D Euclidean Dirac operator considered as Hamiltonian of $4+1$ dimensional disordered system. We use the holographic viewpoint to provide the conjectural explanation of these properties. The delocalization of all modes in the confined phase is related to the $\theta=\pi$ - like phenomena when the domain walls between degenerated vacua are possible. It is conjectured that the localized modes separated by mobility edge from the rest of the spectrum in deconfined QCD correspond to the near-horizon region in the holographic dual.