Dynamics from symmetries in chiral SU(N) gauge theories

Abstract

The symmetries and dynamics of simple chiral SU(N) gauge theories, with matter Weyl fermions in a two-index symmetric tensor and N + 4 anti-fundamental representations, are examined, by taking advantage of the recent developments involving the ideas of generalized symmetries, gauging of discrete center 1-form symmetries and mixed 't Hooft anomalies. This class of models are particularly interesting because the conventional 't Hooft anomaly matching constraints allow a chirally symmetric confining vacuum, with no condensates breaking the U(1) × SU(N + 4) flavor symmetry, and with certain set of massless baryonlike composite fermions saturating all the associated anomaly triangles. Our calculations show that in such a vacuum the UV-IR matching of some 0-form−1form mixed 't Hooft anomalies fails. This implies, for the theories with even N at least, that a chirally symmetric confining vacuum contemplated earlier in the literature actually cannot be realized dynamically. In contrast, a Higgs phase characterized by some gauge-noninvariant bifermion condensates passes our improved scrutiny.

Strong anomaly and phases of chiral gauge theories

“…After this preparation, in section 3 we write the strong-anomaly low-energy effective action for the chiral gauge theories, ψη, χη, as well as all other BY and GG models, following the procedure used for QCD. This discussion confirms the consistency of the dynamical Higgs phase of these models, in agreement with the recent mixed-anomaly study in these chiral gauge theories [25,26], but it actually somewhat strengthens the conclusion. 3 The basic observation is that there is no way of writing the strong-anomaly effective action if confining flavor symmetric vacua are assumed, i.e., by using only the massless baryons (appendices A, C, E, and G).…”

“…To summarize: both the mixed-anomaly analysis [25,26] and the consideration of the strong-anomaly effective action section 3.4, lead to the same conclusion that one of the candidate phase (dynamical Higgs phase) is consistent whereas the other (confining, flavor symmetric phase) is inconsistent, but not that these two phases are inequivalent, perhaps separated by a phase transition of some sort.…”

“…Of course, one of the strongest arguments which discriminates the two candidate vacua comes from the mixed anomalies and the consequent, generalized-anomaly-matching analysis [25,26] (see also [39]). The presence of a mixed anomaly of the type (Z 2 ) F − [Z N ] 2 in the UV theory and the absence of this anomaly in the "symmetric confining phase", show that such a phase cannot be the correct vacuum of the theory [25,26].…”

“…Of course, one of the strongest arguments which discriminates the two candidate vacua comes from the mixed anomalies and the consequent, generalized-anomaly-matching analysis [25,26] (see also [39]). The presence of a mixed anomaly of the type (Z 2 ) F − [Z N ] 2 in the UV theory and the absence of this anomaly in the "symmetric confining phase", show that such a phase cannot be the correct vacuum of the theory [25,26]. As in the ψη model, in the dynamical Higgs phase characterized by the bifermion condensates (4.1), the color-flavor locked Z N symmetry is spontaneousy broken by the condensates, as the U(1) χη symmetry used to form Z N ⊂ U(1) χη × (Z 2 ) F is spontaneously broken.…”

Large $$N_\mathrm{f}$$ for multiple representations

“…They go under the names of Bars-Yankielowicz (BY) [39] and generalized Georgi-Glashow (GG) [40] theories. Their low energy dynamics is still not fully understood in the asymptotically free case with a small number of chiral families [41,42]: indications of the possible allowed phases have been inferred by use of the minimization of degrees of freedom [37,38], or the recent idea of generalized anomalies [43,44]. In this work we are interested in the limit of a large number of fermions, where asymptotic freedom in the UV is lost, and the theory flows to a non-interacting point at low energies.…”