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−1-form 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.
Highlights
In spite of the bulk of knowledge accumulated after almost half-century of studies of vectorlike gauge theories such as SU(3) quantum chromodynamics (QCD), partially based on ever more sophisticated but basically straightforward approximate calculations, as well as some beautiful theoretical developments in models with N = 1 or N = 2 supersymmetries [1]–[5], [6,7,8], surprisingly little is known today about stronglycoupled ordinary chiral gauge theories
The questions we addressed ourselves to are: (i) Do these systems confine, or experience a dynamical Higgs phenomenon? (ii) Do some of them flow into an IR fixed-point CFT? (iii) Does the chiral flavor symmetry remain unbroken, or if spontaneously broken, in which pattern? (iv) If there are more than one apparently possible dynamical scenarios, which one is realized in the infrared? (v) Does the system generate hierarchically disparate mass scales, such as the ones proposed in the “tumbling” scenarios [11]? and so on
In this note we have examined the symmetries of a simple chiral gauge theory, SU(N ) ψη model, by use of the recently found extension of the ’t Hooft anomaly matching constraints, to include the mixed anomalies involving some higher-form symmetries
Summary
A key ingredient of these developments is the idea of “gauging a discrete symmetry”, i.e., identifying the field configurations related by the 1-form (or a higher-form) symmetries, and eliminating the consequent redundancies, effectively modifying the path-integral summation rule over gauge fields [38, 39] Since these generalized symmetries are symmetries of the models considered, even though they act differently from the conventional ones, it is up to us to decide to “gauge” these symmetries. As in the usual application of the ’t Hooft anomalies such as the “anomaly matching” between UV and IR theories, a similar constraint arises in considering the generalized symmetries together with a conventional (“0-form”) symmetry, which has come to be called in recent literature as a “mixed ’t Hooft anomaly” Another term of “global inconsistency” was used to describe a related phenomenon. We shall come back to more general classes of chiral theories in a separate work
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