Universality of random matrices in the microscopic limit and the Dirac operator spectrum

We prove the universality of correlation functions of chiral unitary and unitary ensembles of random matrices in the microscopic limit. The essence of the proof consists in reducing the three-term recursion relation for the relevant orthogonal polynomials into a Bessel equation governing the local asymptotics around the origin. The possible physical interpretation as the universality of soft spectrum of the Dirac operator is briefly discussed. PACS: 05.45.+b, 11.15.Pg, 11.30.Rd e-mail addresses: akemann@itp.uni-hannover.de, y phdamg, z umagnea, x shinsuke@alf.nbi.dk 1 Introduction Consider a four-dimensional gauge theory coupled to fermions in given representations of the gauge group, and with given global (and possibly spontaneously broken) flavor symmetries. In the chiral limit, the associated Dirac operator iD/ anticommutes with fl 5 , fiD/; fl 5 g = 0 : (1.1) This means that the associated eigenvalues of iD/, defined by iD/ OE n = n OE n appear symmetrically around ze..