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Communications in Mathematical Physics

, Volume 102, Issue 2, pp 311–326 | Cite as

Finiteness of Ricci flat supersymmetric non-linear σ-models

  • L. Alvarez-Gaumé
  • P. Ginsparg
Article

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.

Keywords

Neural Network Statistical Physic Complex System Perturbation Theory Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • L. Alvarez-Gaumé
    • 1
  • P. Ginsparg
    • 1
  1. 1.Lyman Laboratory of PhysicsHarvard UniversityCambridgeUSA

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