Effective low-energy theories and QCD Dirac spectra

We analyze the smallest Dirac eigenvalues by formulating an effective theor y for the Dirac spectrum. We find that in a domain where the kinetic term o f the effective theory can be ignored, the Dirac eigenvalues are distribute d according to a Random Matrix Theory with the global symmetries of the QCD partition function. The kinetic term provides information on the slope of the average spectral density of the Dirac operator. In the second half of t his lecture we interpret quenched QCD Dirac spectra (with eigenvalues scatt ered in the complex plane) in terms of an effective tow energy theory.