Instantons and Quark-Mass Generation - The How of Spontaneous Chiral Symmetry Breaking
There is abundant evidence that one of the important characteristics of the physical world is that quarks, if they exist, appear to be massive and so chiral symmetry is spontaneously broken so that is is realized in the Nambu-Goldstone mode. 1) To mention just two pieces of evidence, we point to the absence of parity doubling and the success of PCAC. The leading candidate for a theory of the strong interactions, quantum-chromodynamics2) (QCD), starts out with massless quarks and a chiral SU(N) ⨁ SU(N) symmetry, N being the number of flavors. How the quarks get a mass has been an open question, the importance of which has been stressed in the lecture of Professor Gross. 3) Recently, it was proposed by Callan, Dashen and Gross4) (CDG) that the answer, at least in two space-time dimensions, is provided by instantons and their interactions with fermions. I have found that dynamical quark-mass generation via instantons does occur in four dimensions. 5)
Unable to display preview. Download preview PDF.
- 2.For a review see W. Marciano and H. Pagels, Phys. Rep. C, to be published.Google Scholar
- 3.D.J. Gross, these Proceedings.Google Scholar
- 4.C.G. Callan, R.F. Dashen, and D.J. Gross, IAS Princeton preprint C00-2220–110 (1977).Google Scholar
- 11.C.G. Callan, R.F. Dashen, and D.J. Gross, IAS Princeton preprint (1977).Google Scholar