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Kahler geometry and supersymmetric non-linear σ-models: An introduction

  • Part II: Non-linear σ-Models
  • Conference paper
  • First Online:
Renormalization of Quantum Field Theories with Non-linear Field Transformations

Part of the book series: Lecture Notes in Physics ((LNP,volume 303))

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Abstract

The necessary and sufficent conditions for a supersymmetric extension of a bosonic non-linear a'-model to exist are reviewed. The framework for the perturbative analysis of such models is sketched with emphasis on some delicate points. These are exemplified on the “proof” of all-orders finiteness of hyper-Kahler supersymmetric non linear σ-models.

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References

  1. B. Zumino, Phys.Lett. 87B (1979) 203

    Google Scholar 

  2. L. Alvarez-Gaumé and D.Z. Freedman, Com.Math.Phys. 80 (1981) 443

    Article  Google Scholar 

  3. D.H. Friedan, Phys.Rev.Lett. 45 (1980) 1057 and Ph.D. thesis, August 1980, published in Ann. Phys. 163 (1965) 318

    Article  Google Scholar 

  4. G. Valent, Methods in hyper-Kähler σ-models building,these proceedings

    Google Scholar 

  5. G. Bonneau, Renormalization of bosonic non-linear σ-models built on compact homogeneous manifold, these proceedings

    Google Scholar 

  6. G. Bonneau and F. Delduc, Nucl.Phys. B250 (1985) 561

    Article  Google Scholar 

  7. A detailed introduction to Kähler geometry for physicists can be found in L. Alvarez-Gaumé and D.Z. Freedman lecture at Erice 1980, “Unification of the fundamental particule interactions”, eds. S. Ferrara et all., Plenum New York 1980, page 41

    Google Scholar 

  8. for a more mathematical point of view, see S.Gallot contribution in “première classe de Chern et courbure de Ricci: preuve de laconjecture de Calabi” Société mathématique de France, Astérisque n'58 (1978)

    Google Scholar 

  9. J. Honerkamp, Nucl.Phys. B36 (1972) 130

    Article  Google Scholar 

  10. O. Piguet and K. Sibold, these proceedings

    Google Scholar 

  11. G. Bonneau and F. Delduc, Nucl.Phys. 6266 (1986) 536

    Article  Google Scholar 

  12. B. de Wit and M.T. Grisaru, Phys. Rev. D20 (1979 2082

    Google Scholar 

  13. P.S. Howe, G. Papadopoulos and K.S. Steile, Phys. Lett. 174E (1986) 405

    Google Scholar 

  14. K.S. Stelle,these proceedings

    Google Scholar 

  15. W. Siegel, Phys.Lett. 84B (1979) 193

    Google Scholar 

  16. W. Siegel, Phys.Lett. 94B (1980) 37

    Google Scholar 

  17. L.V. Adveev et all., Phys.Lett. 105E (1981) 272

    Google Scholar 

  18. Unpublished preprints by L. Alvarez-Gaumé and P. Ginsparg, by C.M. Hull

    Google Scholar 

  19. L. Alvarez-Gaumé, S. Coleman and P. Ginsparg, Comm.Math.Phys. 103 (1986) 423

    Article  Google Scholar 

  20. M.T. Grisaru, A.E.M. van de Ven and D. Zanon, Phys.Lett. 173 B (1986) 423

    Google Scholar 

  21. C.M. Pope, these proceedings

    Google Scholar 

  22. L. Alvarez-Gaumé and P. Ginsparg, Comm. Math. Phys. 102 (1985) 311

    Article  Google Scholar 

  23. C.M. Hull, Nucl.Phys. 8260 (1985) 182

    Article  Google Scholar 

  24. For a pedagogical review on Calabi-Yau theorems, see the book refered under[7b)]

    Google Scholar 

  25. A. Galperin et al., Class. Quant. Gravity 2 (1965) 617

    Article  Google Scholar 

  26. D. Maison, these proceedings.

    Google Scholar 

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Authors and Affiliations

  1. Laboratoire de Physique Théorique et Hautes Energies, Université Paris VII, Tour 24, 2 place Jussieu, 75251, Paris Cedex 05, France

    Guy Bonneau

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  1. Guy Bonneau
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Editor information

Peter Breitenlohner Dieter Maison Klaus Sibold

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© 1988 Springer-Verlag

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Bonneau, G. (1988). Kahler geometry and supersymmetric non-linear σ-models: An introduction. In: Breitenlohner, P., Maison, D., Sibold, K. (eds) Renormalization of Quantum Field Theories with Non-linear Field Transformations. Lecture Notes in Physics, vol 303. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0033724

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  • DOI: https://doi.org/10.1007/BFb0033724

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19263-3

  • Online ISBN: 978-3-540-39178-4

  • eBook Packages: Springer Book Archive

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