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The non-linear sigma model in the1 Nexpansion and the inverse scattering transformation in the angular momentum

Authors
Journal
Physics Letters B
0370-2693
Publisher
Elsevier
Publication Date
Volume
98
Issue
4
Identifiers
DOI: 10.1016/0370-2693(81)90015-0

Abstract

Abstract We develop an inverse scattering transformation in the angular momentum to deal with rotationally invariant problems in higher dimensions. We consider the two-dimensional non-linear σ-model in the 1 N expansion. We succeed in expressing the action (a renormalized determinant) in terms of spectral data and we show that no real saddle points exist. This relates to an instability under dilatations connected with the asymptotic freedom of the model. This result together with Zamolodchikov's S-matrix lead us to conjecture that the 1 N series may be convergent for this model.

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