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Spontaneous symmetry breaking in the O(N) model for large N

Coleman, Sidney and Jackiw, R. and Politzer, H. D. (1974) Spontaneous symmetry breaking in the O(N) model for large N. Physical Review D, 10 (8). pp. 2491-2499. ISSN 2470-0010. doi:10.1103/PhysRevD.10.2491.

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We study the O(N) generalization of the σ model in the limit of large N, for four, three, two, and one space-time dimensions. We compute the effective potential and some momentum-dependent Green's functions. In one and two dimensions, spontaneous symmetry breakdown is impossible; any asymmetric minimum inserted in the tree-approximation potential is immediately filled in by the effects of radiative corrections. This is in agreement with general theorems. In four dimensions, the model is inconsistent; it possesses a tachyon. In three dimensions, the model seems to be consistent, and offers an interesting example of some nonlinear effects associated with spontaneous symmetry breakdown that are not present in the usual (tree-approximation) models.

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Politzer, H. D.0000-0002-4983-6621
Additional Information:©1974 The American Physical Society. Received 8 May 1974. Work supported in part by the National Science Foundation under Grant No. GP 40397X and the U.S. Atomic Energy Commission under Contract No. AT(11-1)-3069.
Issue or Number:8
Record Number:CaltechAUTHORS:COLprd74
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9106
Deposited By: Tony Diaz
Deposited On:29 Oct 2007
Last Modified:08 Nov 2021 20:56

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