Quark confinement and the evasion of Goldstone's theorem in 1 + 1 dimensions
Gauge theories of quarks which possess approximate chiral SU(3) x SU(3) symmetry also have approximate U(3) x U(3) symmetry. If the axial symmetries are realized in the Goldstone mode, then one would naively expect a fourth SU(3) singlet pseudoscalar meson with mass comparable to that of the pion. This is contrary to experiment. It has been argued, however, that quark confinement can remove the unwanted Goldstone boson from the physical spectrum of the theory. It is the purpose of this article to shed light on this phenomenon by studying it in a simple setting. We consider the sigma model with minimal electrodynamic coupling in 1+1 dimensions. We confirm that the singlet Goldstone boson is indeed absent although the axial symmetry is spontaneously broken. The would-be massless meson gains a mass from the long-range interactions responsible for confinement. If the Abelian gauge coupling is set to zero, the axial symmetry is no longer spontaneously broken. Using equivalent-boson methods a simple proof of the equivalence of the nonlinear sigma model and the Thirring model (with an additional decoupled massless field) is presented. (AIP)
- Research Organization:
- Laboratory of Nuclear Studies, Cornell University, Ithaca, New York 14853
- Sponsoring Organization:
- USDOE
- NSA Number:
- NSA-33-015873
- OSTI ID:
- 4112800
- Journal Information:
- Phys. Rev., D, v. 12, no. 6, pp. 1742-1753, Journal Name: Phys. Rev., D, v. 12, no. 6, pp. 1742-1753; ISSN PRVDA
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
*QUARK MODEL-- GAUGE INVARIANCE
*QUARKS-- CONFINEMENT
641203*
AXIAL SYMMETRY
CHIRAL SYMMETRY
GLUON MODEL
N64240 --Physics (High Energy)--Particle Interactions & Properties (Theoretical)--Strong (General)
N64330* --Physics (High Energy)--Particle Invariance Principles & Symmetry--Applications (Strong)
S MATRIX
SIGMA MODEL
SU-3 GROUPS
SYMMETRY BREAKING
THIRRING MODEL
TWO-DIMENSIONAL CALCULATIONS
U GROUPS
WARD IDENTITY