, Volume 80, Issue 3, pp 443-451

Geometrical structure and ultraviolet finiteness in the supersymmetric σ-model

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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.

Communicated by A. Jaffe