Mobility edge and Black Hole Horizon

Alexander Gorsky,V.E Volkova,V.A Rubakov,V.A Matveev,Y.V Zhezher,D.G Levkov

doi:10.1051/epjconf/201819105009

Abstract

We conjecture that the mobility edge in the 4D Euclidean Dirac operator spectrum in QCD in the deconfined phase found in the lattice studies corresponds to the near black hole (BH) horizon region in the holographic dual. We present some evidences both from the field theory side and from the worldsheet theory of long open string.

Highlights

In this talk I shall mainly follow the conjectures and questions formulated in [1]
Our study provides some evidences that the mobility edge in the Euclidean 4D Dirac operator spectrum in the deconfined phase of QCD corresponds to the black hole (BH) near horizon region in the holographic dual further clarification is certainly required
It is natural to assume that this correspondence is quite general phenomenon and in particular the 2d BH in the dilaton JT gravity could be dual to SYK model [53](see [54] for review and references) only if we deform it to provide the criticality in its spectrum

Summary

Introduction

In this talk I shall mainly follow the conjectures and questions formulated in [1]. First, let me explain the motivation of our study. One matrix model corresponds to the zero momentum sector of the Chiral Lagrangian while the second model mimics the fermion determinant integrated over the moduli space of a instanton-antiinstanton ensemble in QCD ground state It was suggested in [5] to attack the spectral problem for the Dirac operator by the tools familiar in solid state physics and treat the Euclidean Dirac operator in 4D as the Hamiltonian with respect to the additional fifth time coordinate identified with the Schwinger proper time. On the other hand for the disordered Dirac operator in higher dimensions the spectral density at the origin becomes the order parameter It was argued recently [15] that the non-Anderson disorder driven phase transition takes place if d > 2γ, E ∝ kγ (1).

Dirac operator in QCD

Holographic deconfined QCD

Diagnostics of the critical behavior

Matrix models for localization transition

Conclusion