Communications in Mathematical Physics

, Volume 80, Issue 3, pp 443–451

Geometrical structure and ultraviolet finiteness in the supersymmetric σ-model

  • Luis Alvarez-Gaume
  • Daniel Z. Freedman
Article

DOI: 10.1007/BF01208280

Cite this article as:
Alvarez-Gaume, L. & Freedman, D.Z. Commun.Math. Phys. (1981) 80: 443. doi:10.1007/BF01208280

Abstract

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.

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