Quark Masses and Chiral Symmetry

Abstract

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.

compressed postscript file, 20 pages with 10 figures. Also available at http://penguin.phy.bnl.gov/www/papers/BNL-61796.ps.Z

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• QCD $\theta$-vacua from the chiral limit to the quenched limit
• Quark masses, the Dashen phase, and gauge field topology
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• The U(1) Problem in Chiral Random Matrix Models
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