Patterns of Symmetry Breaking in Chiral "QCD"

Abstract

We consider $SU(N)$ Yang-Mills theory with massless chiral fermions in a complex representation of the gauge group. The main emphasis is on the so-called hybrid psi-chi-eta model. The possible patterns of realization of the continuous chiral flavor symmetry are discussed. We argue that the chiral symmetry is broken in conjunction with a dynamical Higgsing of the gauge group (complete or partial) by bi-fermion condensates. As a result a color-flavor locked symmetry is preserved. The 't Hooft anomaly matching proceeds via saturation of triangles by massless composite fermions or, in a mixed mode, i.e., also by the "weakly" coupled fermions associated with dynamical Abelianization, supplemented by a number of Nambu-Goldstone mesons. Gauge-singlet condensates are of the multifermion type and, though it cannot be excluded, the chiral symmetry realization via such gauge invariant condensates is more contrived (requires a number of four-fermion condensates simultaneously and, even so, problems remain), and less plausible. We conclude that in the model at hand, chiral flavor symmetry implies dynamical Higgsing by bifermion condensates.

Latex 19 pages, 1 figure

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