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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
Article

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.

Keywords

Neural Network Manifold Statistical Physic Complex System Perturbation Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Zumino, B.: Phys. Lett.87 B, 203 (1979)Google Scholar
  2. 2.
    Alvarez-Gaumé, L., Freedman, D.Z.: Phys. Lett.94 B, 171 (1980)Google Scholar
  3. 3.
    Alvarez-Gaumé, L., Freedman, D.Z.: Phys. Rev. D22, 846 (1980)Google Scholar
  4. 4.
    Townsend, P.K., Roĉek, M.: CERN Preprint Th. 2914 (1980)Google Scholar
  5. 5.
    Alvarez-Gaumé, L.: MIT Preprint Nucl. Phys. B (to appear)Google Scholar
  6. 6.
    Friedan, D.: Phys. Rev. Lett.45, 1057 (1980)Google Scholar
  7. 7.
    This result supercedes that of Ref. 1 in that hermiticity is proved rather than assumedGoogle Scholar
  8. 8.
    Calabi, E.: Ann. Soc. l'E.N.S.12, 266 (1979)Google Scholar
  9. 9.
    Gibbons, G.W., Hawking, S.W.: Phys. Lett.78 B, 430 (1978); Hitchin, N.: Proc. Cambridge Philos. Soc.85, 465 (1979)Google Scholar
  10. 10.
    Freedman, D.Z., Townsend, P.K.: Phys. B (to appear)Google Scholar
  11. 11.
    Lichnerowicz, A.: Théorie globale des connections et des groupes d'holonomie, published by Consiglio Nazionale delle Ricerche 1955Google Scholar
  12. 12.
    See Ref. 11, Chap. III for a proof and further detailsGoogle Scholar
  13. 13.
    Chevalley, C.: Theory of Lie Groups, p. 185. Princeton, New Jersey: Princeton Univ. Press 1946Google Scholar
  14. 14.
    Ref. 11, pp. 258–261Google Scholar
  15. 15.
    Alvarez-Gaumé, L., Freedman, D.Z., Mukhi, S.: M.I.T. Preprint (1980)Google Scholar
  16. 16.
    Weinberg, S.: Gravitation and Cosmology, p. 290. New York: John Wiley & Sons, 1972, Eq. (10.9.3) differs from (23) below by an irrelevant infinitesimal diffeomorphismGoogle Scholar
  17. 17.
    DeWit, B., Grisaru, M.T.: Phys. Rev. D20, 2082 (1979)Google Scholar
  18. 18.
    Poggio, E., Pendleton, H.: Phys. Lett.72 B, 200 (1977);Google Scholar
  19. 18a.
    Jones, D.R.T.: Phys. Lett.72 B, 199 (1977)Google Scholar
  20. 19.
    Grisaru, M.T., Roĉek, M., Siegel, W.: Phys. Rev. Lett.45, 1063 (1980)Google Scholar

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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