Introduction to supersymmetry

  • K. S. Stelle
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 181)


The basic features of supersymmetric field theories are presented in this article, emphasizing the structure of the representations of the supersymmetry algebra. In Chapter 1, the simple and N-extended supersymmetry algebras are presented, and the representations on massive and massless states derived using Wigner's method of induced representations. In Chapter 2, the representations of the supersymmetry algebra on fields are introduced, together with the superspace formalism, which is applied to a discussion of the basic supersymmetric model, the Wess-Zumino model. In Chapter 3, supersymmetric Yang-Mills theories are discussed, and the formalism of superspace applied to the quantization of the Wess-Zumino model and supersymmetric Yang-Mills theories, and also to the analysis of the quantum supercurrent for conformally invariant and non-conformally-invariant theories. In Chapter 4, the technique of superspace quantization is applied to the maximal supersymmetic gauge theory, the N=4 supersymmetric Yang-Mills theory. This theory is finite to all orders in perturbation theory, as can be shown using manifestly N=2 supersymmetric Feynman rules.


Chiral Multiplet Supersymmetry Transformation Internal Symmetry Supersymmetry Algebra Auxiliary Field 
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  1. 1.
    S. Coleman and J. Mandula, Phys.Rev. 159 (1967), 1251.Google Scholar
  2. 2.
    Y.A. Gol'fand and E.P. Likhtman, J.E.T.P.Lett. 13 (1971), 323.Google Scholar
  3. 3.
    D.V. Volkov and V.P. Akulov, Phys.Lett. 46B (1973), 109.Google Scholar
  4. 4.
    J. Wess and B. Zumino, Nucl.Phys. B70 (1974), 39; Nucl.Phys. B78 (1974), 1.Google Scholar
  5. 5.
    R. Haag, J.T. Lopuszanski and M.F. Sohnius, Nucl.Phys. B88 (1975), 257.Google Scholar
  6. 6.
    A. Salam and J. Strathdee, Nucl.Phys. B76 (1974), 4778; Nucl.Phys. B84 (1975), 127.Google Scholar
  7. 7.
    S. Ferrara, in Proceedings of the 9th International Conference on General Relativity and Gravitation, Jena, G.D.R. (198); CERN preprint TH-2957 (1980).Google Scholar
  8. 8.
    S. Ferrara, C.A. Savoy and B. Zumino, Phys.Lett. 100B (1981), 393.Google Scholar
  9. 9.
    B.N. Valuyev, JINR Report P2-11638 (1978) (in Russian).Google Scholar
  10. 10.
    F.A. Berezin, The Method of Second Quantization (Academic Press, New York, 1966).Google Scholar
  11. 11.
    S. Ferrara and B. Zumino, Nucl.Phys. B79 (1974), 413.Google Scholar
  12. 11a.
    A. Salam and J. Strathdee, Phys.Lett. 51B (1974), 353.Google Scholar
  13. 11b.
    B. de Wit and D. Freedman, Phys.Rev. D12 (1975), 2286.Google Scholar
  14. 12.
    M.T. Grisaru, W. Siegel and M. Roćek, Nucl.Phys. B159 (1979), 429; M.T. Grisaru and W. Siegel, Nucl.Phys. B187 (1981), 149.Google Scholar
  15. 13.
    M.T. Grisaru and W. Siegel, Nucl.Phys. B201 (1982), 292.Google Scholar
  16. 14.
    W. Siegel, Phys.Lett. 84B (1979), 193.Google Scholar
  17. 14a.
    W. Siegel, P.K. Townsend and P. van Nieuwenhuizen, in Superspace and Supergravity, eds. S.W. Hawking and M. Rocek (Cambridge University Press, 1981). p.165.Google Scholar
  18. 15.
    S. Ferrara, J. Iliopoulos and B. Zumino, Nucl.Phys. B77 (1974), 413.Google Scholar
  19. 16.
    K. Pohlmeyer, Comm.Math.Phys. 27 (1972), 247.Google Scholar
  20. 17.
    S. Ferrara and B. Zumino, Nucl.Phys. B87 (1975), 207.Google Scholar
  21. 18.
    V. Ogievelsky and V. Polubarinov, Sov.J. Nucl.Phys. 4 (1966), 216.Google Scholar
  22. 18a.
    M. Kalb and P. Ramond, Phys.Rev. D9 (1974), 2273.Google Scholar
  23. 19.
    M.T.Grisaru in Recent Developments in Gravitation, eds.M. Levy and S. Deser (Plenum, New York, 1979) p. 577.Google Scholar
  24. 20.
    F. Gliozzi, J. Scherk and D. Olive, Nucl.Phys. B133 (1978), 253.Google Scholar
  25. 20a.
    L. Brink, J. Schwarz and J. Scherk, Nucl.Phys. B121 (1977), 77.Google Scholar
  26. 21.
    M. Rodek and W. Siegel, Phys.Lett. 105B (1981), 275.Google Scholar
  27. 21a.
    V. Rivelles and J.G. Taylor, King's College preprint, London (May 1982).Google Scholar
  28. 22.
    P. Fayet, Nucl.Phys. B149 (1979), 137.Google Scholar
  29. 23.
    O.V. Tarasov and A.A. Vladimirov, Phys.Lett. 96B (1980), 94Google Scholar
  30. 24.
    M.T. Grisaru, M. Rocek and W. Siegel, Phys.Rev.Lett. 45 (1980), 1063.Google Scholar
  31. 25.
    W. Caswell and D. Zanon, Phys.Lett. 100B (1980), 152.Google Scholar
  32. 26.
    M.F. Sohnius and P.C. West, Phys.Lett. 100B (1981), 245. S. Ferrara and B. Zumino, unpublished.Google Scholar
  33. 27.
    K.S. Stelle in Quantum Structure of Space and Time, eds. M.J. Duff and C.J. Isham (Cambridge University Press, 1982), p. 337.Google Scholar
  34. 28.
    P.S. Howe, K.S. Stelle and P.K. Townsend, CERN preprint TH-3271 (1982) (Nucl.Phys. B, in press).Google Scholar
  35. 28a.
    K.S. Stelle, in Proc. 21st Int.Conf. on High Energy Physics, eds. P. Petiau and M. Porneuf, Journal de Physique, Colloque C3 supp. au No 12 (1982), p. 326.Google Scholar
  36. 29.
    P.S. Howe, K.S. Stelle and P.K. Townsend, to appear.Google Scholar
  37. 30.
    S. Mandelstam, in Proc. 21st Int.Conf.on High Energy Physics, eds. P. Petiau and M. Porneuf, Journal de Physique, Colloque C3 Supp. au No 12 (1982), p. 331.Google Scholar
  38. 30a.
    L. Brink, 0. Lindgren and B.E.W. Nilsson, Goteborg preprint UTTG-1-82 (November 1982).Google Scholar
  39. 31.
    See the first paper of reference 11.Google Scholar
  40. 32.
    P. Fayet, Nucl.Phys. B113 (1976), 135.Google Scholar
  41. 33.
    L. Mezincescu, JINR Report P2-12572 (1979).Google Scholar
  42. 34.
    K.S. Stelle in Proc.Conf. on “Group Theoretical Methods in Physics”, Zvenigorod, USSR (November 1982).Google Scholar
  43. 35.
    M.F. Sohnius, Nucl.Phys. B138 (1978), 109.Google Scholar
  44. 35a.
    A. Galperin, E.A. Ivanov and V.I. Ogievetsky, JETP Lett. 33 (1981), 176; JINR Report E2-81-482 (1981).Google Scholar
  45. 36.
    S.L. Adler and W.A. Bardeen, Phys.Rev. 182 (1969), 182.Google Scholar
  46. 37.
    L.V. Avdeev and O.V. Tarasov, Phys.Lett. 112B (1982), 356. *** DIRECT SUPPORT *** A3418138 00007Google Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • K. S. Stelle
    • 1
  1. 1.Blackett LaboratoryImperial CollegeLondon

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