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

Phys. Rev. D 10, 2491 – Published 15 October 1974
Sidney Coleman, R. Jackiw, and H. D. Politzer


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.

DOI: http://dx.doi.org/10.1103/PhysRevD.10.2491

  • Received 8 May 1974
  • Published in the issue dated 15 October 1974

© 1974 The American Physical Society

Authors & Affiliations

Sidney Coleman

  • Lyman Laboratory of Physics, Harvard University, Cambridge, Massachusetts 02138

R. Jackiw

  • Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

H. D. Politzer

  • Lyman Laboratory of Physics, Harvard University, Cambridge, Massachusetts 02138

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