Patterns of symmetry breaking in chiral QCD

Stefano Bolognesi,Kenichi Konishi,Mikhail Shifman

doi:10.1103/physrevd.97.094007

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.

Highlights

AND DISCUSSIONThe pattern of the chiral symmetry breaking in QCD with Nf massless Dirac flavors is well-known. χSB occurs at strong coupling
We argue that the chiral symmetry is broken in conjunction with a dynamical Higgsing of the gauge group by bifermion condensates
The main tool for its analysis is matching the ’t Hooft triangles [1], combined with the large-N limit and the fact that the singlet axial current is internally anomalous. Applying these tools one concludes that the global symmetry SUfðNÞ × SUfðNÞ × Uð1Þ is broken down to the vector subgroup SUfðNÞ × Uð1Þ with

Summary

AND DISCUSSION

The pattern of the chiral symmetry breaking ( χSB) in QCD with Nf massless Dirac flavors is well-known. χSB occurs at strong coupling. The theory (i) on which we focus is asymptotically free, so that the interactions become strong in the infrared, but no gauge-invariant bifermion scalar condensates are possible It possess a nontrivial chiral symmetry Gf 1⁄4 SUð8Þ; the requirement that Gf is either spontaneously broken (entailing the Nambu-Goldstone mesons) or realized linearly in the infrared, combined with the ’t Hooft matching, is so strong that it allows us to determine the most likely dynamical χSB pattern. They differ in the details of colorflavor locked symmetries, but both hinge upon a partial color-flavor diagonal symmetry and a (partial) dynamical Abelianization of the gauge symmetry They collaborate to realize correctly the anomalies associated with the original flavor symmetry SUð8Þ. One is left with the possibility of full Abelianization as the only dynamical scenario for N < 12

Full Abelianization

Remarks

Planar equivalence

WHY CHIRAL SYMMETRY BREAKING PATTERS WITHOUT HIGGSING ARE DISFAVORED

EXTENDED ψχ η MODELS