Abstract
Combining the constraints of Kähler differential geometry with the universality of the normal coordinate expansion in the background field method, we study the ultraviolet behavior of 2-dimensional supersymmetric non-linear σ-models with target space an arbitrary riemannian manifoldM. We show that the constraint ofN=2 supersymmetry requires that all counterterms to the metric beyond one-loop order be cohomologically trivial. It follows that such supersymmetric non-linear σ-models defined on locally symmetric spaces are super-renormalizable and thatN=4 models are on-shell ultraviolet finite to all orders of perturbation theory.
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Alvarez-Gaumé, L., Ginsparg, P. Finiteness of Ricci flat supersymmetric non-linear σ-models. Commun.Math. Phys. 102, 311–326 (1985). https://doi.org/10.1007/BF01229382
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DOI: https://doi.org/10.1007/BF01229382