# Patterns of symmetry breaking in chiral QCD

## 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 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.

- Authors:

- Publication Date:

- Research Org.:
- Univ. of Minnesota, Minneapolis, MN (United States); Univ. of California, Santa Barbara, CA (United States); Univ. of Pisa (Italy)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF); National Inst. of Nuclear Physics (INFN) (Italy)

- OSTI Identifier:
- 1436832

- Alternate Identifier(s):
- OSTI ID: 1503898

- Grant/Contract Number:
- SC0011842; PHY-1125915

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 97 Journal Issue: 9; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; anomalies; composite models; dynamical symmetry breaking models

### Citation Formats

```
Bolognesi, Stefano, Konishi, Kenichi, and Shifman, Mikhail. Patterns of symmetry breaking in chiral QCD. United States: N. p., 2018.
Web. https://doi.org/10.1103/PhysRevD.97.094007.
```

```
Bolognesi, Stefano, Konishi, Kenichi, & Shifman, Mikhail. Patterns of symmetry breaking in chiral QCD. United States. https://doi.org/10.1103/PhysRevD.97.094007
```

```
Bolognesi, Stefano, Konishi, Kenichi, and Shifman, Mikhail. Thu .
"Patterns of symmetry breaking in chiral QCD". United States. https://doi.org/10.1103/PhysRevD.97.094007.
```

```
@article{osti_1436832,
```

title = {Patterns of symmetry breaking in chiral QCD},

author = {Bolognesi, Stefano and Konishi, Kenichi and Shifman, Mikhail},

abstractNote = {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 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.},

doi = {10.1103/PhysRevD.97.094007},

journal = {Physical Review D},

number = 9,

volume = 97,

place = {United States},

year = {2018},

month = {5}

}

https://doi.org/10.1103/PhysRevD.97.094007

*Citation information provided by*

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Web of Science

#### Figures / Tables:

*N*in the plane (

*N*).

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Works referencing / citing this record:

##
Dynamics and symmetries in chiral $SU\mathbf{(}N\mathbf{)}$ gauge theories

journal, December 2019

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*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*