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Renormalizability and infrared finiteness of non-linear σ-models: A regularization-independent analysis for compact coset spaces

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Abstract

The non-linearσ models in two space-time dimensions corresponding to compact homogeneous coset spacesG/H are studied with particular attention to three problems: first, independence of coordinate choice and regularization, second, the physical content of the theory, and finally the regularity of the “physics” in the infrared limit. Concerning in particular the physical content of the theory, we construct a set of local observables whose correlation functions depend on a finite number of parameters identified among those defining the metric tensor of the coset space. For these models, we give a general proof of renormalizability based on the introduction of a nilpotent BRS operator which describes the non-linear isometries and a classical action which contains a mass term for all quantized fields. The mass term belongs to a finite dimensional representation of the groupG, which allows us to prove the conjecture that the correlation functions of local observables, i.e., the local operators invariant underG, are regular in the infrared limit.

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Author notes

  1. C. Becchi & A. Blasi

    Present address: Dipartimento di Fisica dell'Università di Genova and INFN, Sezione di Genova, Via Dodecaneso 33, I-16146, Genova, Italy

  2. F. Delduc

    Present address: Laboratoire de Physique Théorique et Hautes Energies, Université Paris VII et CNRS (UA 280), 2 place Jussieu, Tour 24, F-75251, Paris Cedex 05, France

Authors and Affiliations

  1. CERN, CH-1211, Geneva 23, Switzerland

    C. Becchi, A. Blasi & F. Delduc

  2. Dipartimento di Fisica dell'Università di Genova and INFN, Sezione di Genova, Via Dodecaneso 33, I-16146, Genova, Italy

    R. Collina

  3. Laboratoire de Physique Théorique et Hautes Energies, Université Paris VII et CNRS (UA 280), 2 place Jussieu, Tour 24, F-75251, Paris Cedex 05, France

    G. Bonneau

Authors
  1. C. Becchi
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  2. A. Blasi
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  3. G. Bonneau
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  4. R. Collina
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  5. F. Delduc
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Additional information

Communicated by L. Alvarez-Gaumé

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Becchi, C., Blasi, A., Bonneau, G. et al. Renormalizability and infrared finiteness of non-linear σ-models: A regularization-independent analysis for compact coset spaces. Commun.Math. Phys. 120, 121–148 (1988). https://doi.org/10.1007/BF01223209

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  • DOI: https://doi.org/10.1007/BF01223209

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