The spectral density of the QCD Dirac operator and patterns of chiral symmetry breaking

We Study the spectrum of the QCD Dirac operator for two colors with fermion s in the fundamental representation and for two or more colors with adjoint fermions. For Nc flavors, the chiral flavor symmetry of these theories is spontaneously broken according to SU(2N(f)) --> Sp (2N(f)) and SU(N-f) --> O(N-f), respectively, rather than the symmetry breaking pattern SU(N-f) x S U(N-f) --> SU(Nf) for QCD with three or more colors and fundamental fermion s. In this paper we study the Dirac spectrum for the first two symmetry bre aking patterns: Following previous work for the third case we find the Dira c spectrum in the domain lambda << Lambda(QCD) by means of partially quench ed chiral perturbation theory. In particular, this result allows us to calc ulate the slope of the Dirac spectrum at lambda = 0. We also show that for lambda << 1/L(2)Lambda(QCD) (with L the linear size of the system) the Dira c spectrum is given by a chiral Random Matrix Theory with the symmetries of the Dirac operator. (C) 1999 Elsevier Science B.V. All rights reserved.