High Energy Physics Seminars

The partition functions of gauge theories with spontaneously broken chiral symmetries are analyzed for an arbitrary number of flavors, N_f, and arbitrary quark masses including the contributions from all topological sectors in the Leutwyler--Smilga regime. In the Leutwyler--Smilga regime, the theories only depend on simple combinations of quark masses, volume, chiral condensate and vacuum angle. We consider the cases of quarks in the adjoint and fundamental representation separately. For two and three flavors, the heta dependence of the QCD vacuum is studied in detail. We find a discontinuity at heta=pi in the first derivative of the energy density with respect to heta for degenerate quark masses. This corresponds to the first--order phase transition in which CP is spontaneously broken, known as Dashen's phenomena. We derive simple expressions for the chiral condensate and the topological density and show that they are in fact related. By examining the zeros of the various partition functions, we elucidate the mechanism leading to Dashen's phenomena in QCD.