Spontaneous symmetry breaking in theO(N)model for largeN
Abstract
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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Tunnelling between degenerate vacua is at the origin of convexity of the effective potential and restoration of a symmetric true vacuum.
“while the second is at the origin of convexity of the effective potential [2-11] and therefore restoration of a symmetric true vacuum.”
From Double-well instantons in finite volume (2024) · cites this paper as [3]
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Phase transitions in quantum chromodynamics
Meyer-Ortmanns, H. (1996) · Reviews of Modern Physics · doi:10.1103/revmodphys.68.473 · Cited by 161 · see citing works
Symmetry restoration, tunneling, and the null energy condition
Alexandre, J., & Polonyi, J. (2022) · Physical Review D · doi:10.1103/physrevd.106.065008 · Cited by 8 · see citing works
Double-well instantons in finite volume
Ai, W.-Y., Alexandre, J., Carosi, M., Garbrecht, B., & Pla, S. (2024) · Journal of High Energy Physics · doi:10.1007/jhep05(2024)099 · Cited by 6 · see citing works
- Authors
- Coleman, S., Jackiw, R., & Politzer, H. D.
- Affiliations
- Harvard University (US)
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 1974-10-15
- Volume
- 10
- Issue
- 8
- Pages
- 2491-2499
- ISSN
- 0556-2821 (ISSN-L)
- OpenAlex
- W2120309232
- Cited by
- 469
- References
- 0
- Citations by year
- 2026: 5 · 2025: 7 · 2024: 10 · 2023: 18 · 2022: 17 · 2021: 7 · 2020: 29 · 2019: 7 · 2018: 8 · 2017: 4 · 2016: 6 · 2015: 4 · 2014: 12 · 2013: 11 · 2012: 8
- FWCI
- 17.02
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- CaltechAUTHORS (California Institute of Technology) (submittedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Particle physics theoretical and experimental studies
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Quantum Chromodynamics and Particle Interactions
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Keywords
- spontaneous symmetry breaking, O(N) nonlinear sigma model, large N limit, effective potential, radiative corrections, tachyons, nonlinear effects, tree approximation, dimensional analysis
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