Effective field theories in the large-N limit
- Theory Group, Department of Physics, University of Texas, Austin, Texas 78712 (United States)
Various effective field theories in four dimensions are shown to have exact nontrivial solutions in the limit as the number N of fields of some type becomes large. These include extended versions of the U (N) Gross-Neveu model, the nonlinear O(N) {sigma} model, and the CP{sup N{minus}1} model. Although these models are not renormalizable in the usual sense, the infinite number of coupling types allows a complete cancellation of infinities. These models provide qualitative predictions of the form of scattering amplitudes for arbitrary momenta, but because of the infinite number of free parameters, it is possible to derive quantitative predictions only in the limit of small momenta. For small momenta the large-N limit provides only a modest simplification, removing at most a finite number of diagrams to each order in momenta, except near phase transitions, where it reduces the infinite number of diagrams that contribute for low momenta to a finite number. {copyright} {ital 1997} {ital The American Physical Society}
- OSTI ID:
- 538668
- Journal Information:
- Physical Review, D, Vol. 56, Issue 4; Other Information: PBD: Aug 1997
- Country of Publication:
- United States
- Language:
- English
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