Metal or Insulator? Dirac operator spectrum in holographic QCD

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.