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Title: 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}
}

Technical Report:

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