# 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. doi: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*

Web of Science

Web of Science

#### Figures / Tables:

*N*in the plane (

*N*).

_{ψ}; N_{χ}Works referenced in this record:

##
Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions

journal, September 2009

- Ünsal, Mithat
- Physical Review D, Vol. 80, Issue 6

##
Yang-Mills theories with chiral matter at strong coupling

journal, May 2009

- Shifman, M.; Ünsal, Mithat
- Physical Review D, Vol. 79, Issue 10

##
Phases of chiral gauge theories

journal, May 2000

- Appelquist, Thomas; Duan, Zhiyong; Sannino, Francesco
- Physical Review D, Vol. 61, Issue 12

##
Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD

journal, December 1994

- Seiberg, N.; Witten, E.
- Nuclear Physics B, Vol. 431, Issue 3

##
Chiral Lattice Gauge Theories via Mirror–Fermion Decoupling: a Mission (Im)Possible?

journal, June 2010

- Poppitz, Erich; Shang, Yanwen
- International Journal of Modern Physics A, Vol. 25, Issue 14

##
New constraints on chiral gauge theories

journal, July 1999

- Appelquist, Thomas; Cohen, Andrew; Schmaltz, Martin
- Physics Letters B, Vol. 459, Issue 1-3

##
Tumbling gauge theories

journal, July 1980

- Raby, Stuart; Dimopoulos, Savas; Susskind, Leonard
- Nuclear Physics B, Vol. 169, Issue 5-6

##
${A}_{k}\overline{F}$ chiral gauge theories

journal, November 2015

- Shi, Yan-Liang; Shrock, Robert
- Physical Review D, Vol. 92, Issue 10

##
Chiral $\mathrm{SU}(N)$ gauge theory planar equivalent to super-Yang-Mills theory

journal, May 2012

- Armoni, A.; Shifman, M.
- Physical Review D, Vol. 85, Issue 10

##
Fradkin–Shenker continuity and “instead-of-confinement” phase

journal, September 2017

- Shifman, M.; Yung, A.
- Modern Physics Letters A, Vol. 32, Issue 30

##
Center-stabilized Yang-Mills theory: Confinement and large $N$ volume independence

journal, September 2008

- Ünsal, Mithat; Yaffe, Laurence G.
- Physical Review D, Vol. 78, Issue 6

##
QCD-like theories on ${R}_{3}\times {S}_{1}$ : A smooth journey from small to large $r({S}_{1})$ with double-trace deformations

journal, September 2008

- Shifman, M.; Ünsal, Mithat
- Physical Review D, Vol. 78, Issue 6

##
Phase diagrams of lattice gauge theories with Higgs fields

journal, June 1979

- Fradkin, Eduardo; Shenker, Stephen H.
- Physical Review D, Vol. 19, Issue 12

##
Planar limit of orientifold field theories and emergent center symmetry

journal, February 2008

- Armoni, Adi; Shifman, Mikhail; Ünsal, Mithat
- Physical Review D, Vol. 77, Issue 4

##
Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory

journal, September 1994

- Seiberg, N.; Witten, E.
- Nuclear Physics B, Vol. 426, Issue 1

##
Renormalization-group evolution and nonperturbative behavior of chiral gauge theories with fermions in higher-dimensional representations

journal, December 2015

- Shi, Yan-Liang; Shrock, Robert
- Physical Review D, Vol. 92, Issue 12

Works referencing / citing this record:

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

journal, December 2019

- Bolognesi, Stefano; Konishi, Kenichi
- Physical Review D, Vol. 100, Issue 11

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