# Instantons and massless fermions in two dimensions

## Abstract

The role of instantons in the breakdown of chiral U(N) symmetry is studied in a two dimensional model. Chiral U(1) is always destroyed by the axial vector anomaly. For N = 2 chiral SU(N) is also spontaneously broken yielding massive fermions and three (decoupled) Goldstone bosons. For N greater than or equal to 3 the fermions remain massless. Realistic four dimensional theories are believed to behave in a similar way but the critical N above which the fermions cease to be massive is not known in four dimensions.

- Authors:

- Publication Date:

- Research Org.:
- Institute for Advanced Study, Princeton, N.J. (USA); Princeton Univ., N.J. (USA). Joseph Henry Labs.

- OSTI Identifier:
- 7284867

- Report Number(s):
- COO-2220-110

TRN: 77-019892

- DOE Contract Number:
- EY-76-S-02-2220

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CHIRAL SYMMETRY; SYMMETRY BREAKING; U GROUPS; FERMIONS; FOUR-DIMENSIONAL CALCULATIONS; GOLDSTONE BOSONS; TWO-DIMENSIONAL CALCULATIONS; U-1 GROUPS; VECTORS; BOSONS; ELEMENTARY PARTICLES; LIE GROUPS; POSTULATED PARTICLES; SYMMETRY; SYMMETRY GROUPS; TENSORS; 645301* - High Energy Physics- Particle Invariance Principles & Symmetries- General- (-1987)

### Citation Formats

```
Callan, C.G. Jr., Dashen, R., and Gross, D.J..
```*Instantons and massless fermions in two dimensions*. United States: N. p., 1977.
Web. doi:10.2172/7284867.

```
Callan, C.G. Jr., Dashen, R., & Gross, D.J..
```*Instantons and massless fermions in two dimensions*. United States. doi:10.2172/7284867.

```
Callan, C.G. Jr., Dashen, R., and Gross, D.J.. Sun .
"Instantons and massless fermions in two dimensions". United States.
doi:10.2172/7284867. https://www.osti.gov/servlets/purl/7284867.
```

```
@article{osti_7284867,
```

title = {Instantons and massless fermions in two dimensions},

author = {Callan, C.G. Jr. and Dashen, R. and Gross, D.J.},

abstractNote = {The role of instantons in the breakdown of chiral U(N) symmetry is studied in a two dimensional model. Chiral U(1) is always destroyed by the axial vector anomaly. For N = 2 chiral SU(N) is also spontaneously broken yielding massive fermions and three (decoupled) Goldstone bosons. For N greater than or equal to 3 the fermions remain massless. Realistic four dimensional theories are believed to behave in a similar way but the critical N above which the fermions cease to be massive is not known in four dimensions.},

doi = {10.2172/7284867},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Sun May 01 00:00:00 EDT 1977},

month = {Sun May 01 00:00:00 EDT 1977}

}

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