The chiral transition as an Anderson transition

Abstract

At low temperature the low-lying QCD Dirac spectrum obeys random matrix statistics. Recently we found that above $T_{c}$ the lowest part of the spectrum consists of localized modes that obey Poisson statistics. An interesting implication of this is that as the system crosses $T_{c}$ from above, the spectral statistics at $\lambda=0$ changes from Poisson to random matrix. Here we study this transition and its possible implications for the finite temperature transition of QCD-like theories.