Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2008-12-01
Physics
High Energy Physics
High Energy Physics - Phenomenology
28 pages, i figure. Presented at Approaches to QCD, Oberwoelz, Austria, Sept. 2008
Scientific paper
The functional Schrodinger equation (FSE) for QCD gives a unique perspective on generation of a gluon mass m, as required for center vortices. The FSE, which yields a special d=3 gauge action, combined with lattice calculations strictly in d=3 give a value for the dimensionless ratio of d=3 coupling to mass g_3^2/m. From this we infer a reasonably accurate value for the d=4 running coupling g^2(0) in the region of low momentum where it is nearly constant. The result, consistent with other estimates, is too low to drive chiral symmetry breaking (CSB) for quarks in a standard gap equation that has no explicit confinement effects. We recall and improve on old work showing that confinement implies CSB for quarks, and consider CSB for test (that is, quenched) Dirac fermions in the adjoint representation. Here the previously-found value of $g^2(0)$ is large enough to drive CSB in a gap equation, which we relate to the presence of center vortices (non-confining, for the adjoint) and nexuses that drive fermionic zero modes. We discuss the extension of adjoint CSB to finite temperature.
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