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