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 ψχη 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 bifermion 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.
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We would like to thank R. Shrock and E. Poppitz who drew our attention to [3,4] and a number of related publications. Their input was very important. The work of M. S. was supported in part by the DOE Grant No. DE-SC 0011842 and by the National Science Foundation under Grant No. NSF PHY-1125915. M. S. is grateful to KITP where this paper was completed for the kind hospitality extended to him during the workshop “Resurgent Asymptotics in Physics and Mathematics.” The work of S.B and K. K. is supported by the INFN special project grant “GAST (Gauge and String Theory)”. M. S. thanks INFN, Pisa and University of Pisa for the warm hospitality received during his visit to Pisa, when the collaboration on the present work started.
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