Abstract
We present a simple argument which seems to favor, when applied to a large class of strongly-coupled chiral gauge theories, a dynamical-Higgs-phase scenario, characterized by certain bifermion condensates. Flavor symmetric confining vacua described in the infrared by a set of baryonlike massless composite fermions saturating the conventional ’t Hooft anomaly matching equations, appear instead disfavored. Our basic criterion is that it should be possible to write a strong-anomaly effective action, analogous to the one used in QCD to describe the solution of the U(1)A problem in the low-energy effective action, by using the low-energy degrees of freedom in the hypothesized infrared theory. We also comment on some well-known ideas such as the complementarity and the large N planar dominance in the context of these chiral gauge theories. Some striking analogies and contrasts between the massless QCD and chiral gauge theories seem to emerge from this discussion.
Highlights
Our comprehension of the dynamics of strongly-coupled chiral gauge theories is still largely unsatisfactory, in spite of their potential role in describing the physics of fundamental interactions beyond the standard model
We present a simple argument which seems to favor, when applied to a large class of strongly-coupled chiral gauge theories, a dynamical-Higgs-phase scenario, characterized by certain bifermion condensates
Supporting the conclusion of [25, 26]: the system is in dynamical Higgs phase in the Bars-Yankielowicz and Georgi-Glashow models
Summary
Our comprehension of the dynamics of strongly-coupled chiral gauge theories is still largely unsatisfactory, in spite of their potential role in describing the physics of fundamental interactions beyond the standard model. From the point of view of renormalization group, assuming that the color interactions become strongly coupled towards the infrared, and that the low-energy effective degrees of freedom are not the original gluons and quarks (and similar color gauge bosons and matter fermions in general chiral theories), the anomalies present in the underlying theory must be reproduced for consistency either by composite massless fermions (’t Hooft) if the symmetry remains unbroken, or, if spontaneously broken, by massless Nambu-Goldstone (NG) bosons. More general Bars-Yankielowicz and Georgi-Glasow models, which are similar to the above two models but with p additional pairs of fermions in the fundamental and antifundamental representations, will be considered In all these models the conventional ’t Hooft anomaly matching discussion apparently allows a confining phase, with no condensates and with full unbroken global symmetry, with some simple set of massless composite fermions saturating the anomaly matching equations. The constant Fπ represents the amplitude for the broken current to produce the pion from the vacuum (the pion decay constant)
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