Spectral Fluctuations of the QCD Dirac Operator

Abstract

It is generally believed that QCD with massless quarks undergoes a chiral phase transition (see [1] for a review). This

leads to important observable signatures in the real world with two light quarks. The order parameter of the chiral phase transition is the chiral condensate (Ψ̄Ψ), is directly related to the average spectral density of the Dirac operator [2]. However, the eigenvalues of the Dirac operator fluctuate about their average position. The question we wish to address in this lecture is to what extent such fluctuations are universal. If that is the case, they do not depend on the full QCD dynamics and can be obtained from a much simpler chiral Random Matrix Theory (chRMT) with the global symmetries of the QCD partition function.