Muti-Flavor Dirac Fermions in a Random Vector Potential: Lattice Supersymmetry and Localization

In the previous paper we studied Dirac fermions in a non-Abelian random vector potential by using lattice supersymmetry. By the lattice regularization, the system of disordered Dirac fermions is defined without any ambiguities. We showed there that at strong-disorder limit correlation function of the fermion local density of states decays algebraically at the band center. In this paper, we shall reexamine the multiflavor or multi-species case rather in detail and argue that the correlator at the band center decays exponentially for the case of a large number of flavors. This means that a delocalization-localization phase transition occurs as the number of flavors is increased. This discussion is supported by the recent numerical studied on multiflavor QCD at the strong-coupling limit, which shows that the phase structure of QCD drastically changes depending on the number of flavors. The above behaviour of the correlator of the random Dirac fermions is closely related with how the chiral symmetry is realized in QCD. PACS: 72.15.Rn; 73.20.Jc; 11.15.Ha e-mail address: [email protected] 1