## A symmetry breaking scenario for QCD _{3}

## Abstract

We consider the dynamics of 2+1 dimensional SU(N) gauge theory with Chern-Simons level k and N _{ƒ} fundamental fermions. By requiring consistency with previously suggested dualities for N _{ƒ} ≤ 2k as well as the dynamics at k = 0 we propose that the theory with N f > 2k breaks the U(N f ) global symmetry spontaneously to U(N _{ƒ}/2 + k) × U(N _{ƒ}/2 - k). In contrast to the 3+1 dimensional case, the symmetry breaking takes place in a range of quark masses and not just at one point. The target space never becomes parametrically large and the Nambu-Goldstone bosons are therefore not visible semi-classically. Such symmetry breaking is argued to take place in some intermediate range of the number of flavors, 2k < N _{ƒ} < N _{*}(N, k), with the upper limit N _{*} obeying various constraints. The Lagrangian for the Nambu-Goldstone bosons has to be supplemented by nontrivial Wess-Zumino terms that are necessary for the consistency of the picture, even at k = 0. Furthermore, we suggest two scalar dual theories in this range of N _{ƒ}. A similar picture is developed for SO(N) and Sp(N) gauge theories. It sheds new light on monopolemore »

- Authors:

- Weizmann Inst. of Science, Rehovot (Israel). Dept. of Particle Physics and Astrophysics; Stony Brook Univ., NY (United States). Simons Center for Geometry and Physics
- Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences

- Publication Date:

- Research Org.:
- Inst. for Advanced Study, Princeton, NJ (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1502465

- Grant/Contract Number:
- SC0009988

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 1; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Chern-Simons Theories, Duality in Gauge Field Theories, Global Symmetries, Anomalies in Field and String Theories

### Citation Formats

```
Komargodski, Zohar, and Seiberg, Nathan. A symmetry breaking scenario for QCD3. United States: N. p., 2018.
Web. doi:10.1007/jhep01(2018)109.
```

```
Komargodski, Zohar, & Seiberg, Nathan. A symmetry breaking scenario for QCD3. United States. doi:10.1007/jhep01(2018)109.
```

```
Komargodski, Zohar, and Seiberg, Nathan. Tue .
"A symmetry breaking scenario for QCD3". United States. doi:10.1007/jhep01(2018)109. https://www.osti.gov/servlets/purl/1502465.
```

```
@article{osti_1502465,
```

title = {A symmetry breaking scenario for QCD3},

author = {Komargodski, Zohar and Seiberg, Nathan},

abstractNote = {We consider the dynamics of 2+1 dimensional SU(N) gauge theory with Chern-Simons level k and Nƒ fundamental fermions. By requiring consistency with previously suggested dualities for Nƒ ≤ 2k as well as the dynamics at k = 0 we propose that the theory with N f > 2k breaks the U(N f ) global symmetry spontaneously to U(Nƒ/2 + k) × U(Nƒ/2 - k). In contrast to the 3+1 dimensional case, the symmetry breaking takes place in a range of quark masses and not just at one point. The target space never becomes parametrically large and the Nambu-Goldstone bosons are therefore not visible semi-classically. Such symmetry breaking is argued to take place in some intermediate range of the number of flavors, 2k < Nƒ < N*(N, k), with the upper limit N* obeying various constraints. The Lagrangian for the Nambu-Goldstone bosons has to be supplemented by nontrivial Wess-Zumino terms that are necessary for the consistency of the picture, even at k = 0. Furthermore, we suggest two scalar dual theories in this range of Nƒ. A similar picture is developed for SO(N) and Sp(N) gauge theories. It sheds new light on monopole condensation and confinement in the SO(N) & Spin(N) theories.},

doi = {10.1007/jhep01(2018)109},

journal = {Journal of High Energy Physics (Online)},

number = 1,

volume = 2018,

place = {United States},

year = {2018},

month = {1}

}

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