Communications in Mathematical Physics

, Volume 80, Issue 3, pp 443–451 | Cite as

Geometrical structure and ultraviolet finiteness in the supersymmetric σ-model

  • Luis Alvarez-Gaume
  • Daniel Z. Freedman


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.


Neural Network Manifold Statistical Physic Complex System Perturbation Theory 
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Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Luis Alvarez-Gaume
    • 1
    • 2
  • Daniel Z. Freedman
    • 1
    • 2
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Institute for Theoretical PhysicsState University of New YorkStony BrookUSA

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