Quark Masses and Chiral Symmetry

I discuss the global structure of the strongly interacting gauge theory of quarks and gluons as a function of the quark masses and the CP violating parameter $\theta$. I concentrate on whether a first order phase transition occurs at $\theta=\pi.$ I show why this is expected when multiple flavors have a small degenerate mass. This transition can be removed by sufficient flavor-breaking. I speculate on the implications of this structure for Wilson's lattice fermions.