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Geometrical structure and ultraviolet finiteness in the supersymmetric σ-model

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Abstract

A complete geometrical classification of supersymmetric σ-models is given. Extended supersymmetry requires covariantly constant complex structures, and Kahler and hyperkahler manifolds play a special role. As an application of the classification, it is shown that a particular class of these models is on-shell ultraviolet finite to all orders in perturbation theory.

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Authors and Affiliations

  1. Department of Mathematics, Massachusetts Institute of Technology, 02139, Cambridge, MA, USA

    Luis Alvarez-Gaume & Daniel Z. Freedman

  2. Institute for Theoretical Physics, State University of New York, 11794, Stony Brook, NY, USA

    Luis Alvarez-Gaume & Daniel Z. Freedman

Authors
  1. Luis Alvarez-Gaume
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  2. Daniel Z. Freedman
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Communicated by A. Jaffe

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Alvarez-Gaume, L., Freedman, D.Z. Geometrical structure and ultraviolet finiteness in the supersymmetric σ-model. Commun.Math. Phys. 80, 443–451 (1981). https://doi.org/10.1007/BF01208280

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  • DOI: https://doi.org/10.1007/BF01208280

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