PUB - Publikationen an der Universität Bielefeld

We describe in detail the solution of the extension of the chiral GaussianUnitary Ensemble (chGUE) into the complex plane. The correlation functions ofthe model are first calculated for a finite number of N complex eigenvalues,where we exploit the existence of orthogonal Laguerre polynomials in thecomplex plane. When taking the large-N limit we derive new correlationfunctions in the case of weak and strong non-Hermiticity, thus describing thetransition from the chGUE to a generalized Ginibre ensemble. Applications tothe Dirac operator eigenvalue spectrum in QCD with non-vanishing chemicalpotential are briefly discussed. This is an extended version ofarXiv:hep-th/0204068.