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Extended Supersymmetry and Extended Supergravity Theories

  • J. Scherk
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 44)

Abstract

The failure of quantized gravity in interaction with quantized matter fields (whether scalar, spinor of vector fields) to provide renormalizable results even at the one loop level [1] has led to a situation analoguous to the puzzle of the V-A theory of weak interactions before the advent of gauge theories. The V-A theory of weak interactions was known to be correct at the tree approximation, but having a coupling constant whose dimension was the inverse of a mass squared (GF = 1. 01 10−5GeV−2) it was giving divergent and non renormalizable answers even at the one loop level. In a similar fashion, classical general relativity is known to describe gravity accurately, but quantum gravity leads to divergent results, except in the one loop case and for pure gravity [l]. The analogy with the V-A theory of weak interactions is even stronger if one remarks that the coupling constant of gravity also has the dimension of the inverse of a mass \(\left( {K \sim \,\left( {{G_N}} \right)\frac{1}{2}\, \sim \,.8\,{{10}^{ - 19}}\,Ge{V^{ - 1}}} \right)\). One can think that the trouble with quantized gravity is due to the perturbative approach rather than with the theory itself. The other possibility is to look for alternative theories of gravity which would be free of divergences.

Keywords

Open String Supergravity Theory Supersymmetry Transformation Duality Transformation Supersymmetry Algebra 
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]
    G. ‘t Hooft and M. Veltman, Ann. Inst. K. Poincaré 20 (1974) 69Google Scholar
  2. S. Deser, H.S. Tsao and P. Van Nieuwenhuizen, Phys. Rev. D10 (1974) 3337ADSGoogle Scholar
  3. For a general review of results obtained in quantum gravity, see P. Van Nieuwenhuizen in Proceedings of the Marcel Grossmann Meeting (1976) published by North Holland Co.Google Scholar
  4. [2]
    D.Z. Freedman, P. Van Nieuwenhuizen and S. Ferrara, Phys. Rev. D13 (1976) 3214MathSciNetADSGoogle Scholar
  5. S. Deser and B. Zumino, Phys. Lett. 62B (1976) 335MathSciNetGoogle Scholar
  6. [3]
    S. Ferrara and P. Van Nieuwenhuizen, Phys. Rev. Letters 37 (1976) 1669ADSCrossRefGoogle Scholar
  7. [4]
    D.Z. Freedman, Phys. Lett. 38 (1977) 105CrossRefGoogle Scholar
  8. S. Ferrara, J. Seherk and B. Zumino, Phys. Lett. 66B (1977) 35Google Scholar
  9. [5]
    A. Das, Phys. Rev. D15 (1977) 2805ADSGoogle Scholar
  10. [6]
    E. Cremmer, J. Scherk and S. Ferrara, Phys. Lett 68B (1977) 234MathSciNetGoogle Scholar
  11. [7]
    E. Cremmer and J. Scherk, Nucl. Phys. B127 (1977) 259MathSciNetADSCrossRefGoogle Scholar
  12. [8]
    E. Cremmer, J. Scherk and S. Ferrara, Phys. Lett. 74B (1978) 61Google Scholar
  13. [9]
    B. de Wit and D.Z. Freedman, Nucl. Phys. B130 (1977) 105ADSCrossRefGoogle Scholar
  14. [10]
    D.Z. Freedman and A. Das, Nucl. Phys. B120 (1977) 221MathSciNetADSCrossRefGoogle Scholar
  15. [11]
    M.T. Grisaru, P. Van Nieuwenhuizen and J.A.M. Vermaseren, Phys. Rev.’ Lett. 37 (1976) 1662Google Scholar
  16. S. Deser, J. Kay and K. Stelle, Phys. Rev. Lett. 38 (1977) 527ADSCrossRefGoogle Scholar
  17. P. Van Nieuwenhuizen and J.A.M. Vermaseren, Phys. Rev. D16 (1977)298Google Scholar
  18. For a review see P. Van Nieuwenhuizen, CERN preprint TH 2473 (1978) invited talk at the Orbis Scientiae Coral Gables, 1978Google Scholar
  19. [12]
    S. Deser and J.H. Kay, Phys. Lett. 76B (1978) 400MathSciNetGoogle Scholar
  20. [13]
    P. Ramond, Phys. Rev. D3 (1971) 2415MathSciNetADSGoogle Scholar
  21. A. Neveu and J.H. Schwarz, Nucl. Phys. B31 (1971) 86, Phys. Rev. D4 (1971) 1109Google Scholar
  22. A. Neveu and J.H. Schwarz and C.B. Thorn, Phys. Lett. 35B (1971) 521Google Scholar
  23. [14]
    Dual Theory” edited by M. Jacob, North Holland Pub. Co. (1974)Google Scholar
  24. J. Scherk, Rev. Mod. Phys. 47 (1975) 123MathSciNetADSCrossRefGoogle Scholar
  25. [l5]
    F. Gliozzi, J. Scherk and D. Olive, Phys. Lett. 65B (1976) 282Google Scholar
  26. [16]
    F. Gliozzi, J. Scherk and D. Olive, Nucl. Phys. B122 (1977) 253ADSCrossRefGoogle Scholar
  27. [17]
    L. Brink, J.H. Schwarz and J. Scherk, Nucl. Phys. B121 (1977) 77MathSciNetADSCrossRefGoogle Scholar
  28. [18]
    S. Ferrara, J. Scherk and B. Zumino, Nucl. Phys. B121 (1977) 293CrossRefGoogle Scholar
  29. l9] C.K. Zachos, Phys. Lett. 76B (1978) 329 and unpublished workGoogle Scholar
  30. [20]
    E. Cremmer and J. Scherk, Nucl. Phys. B103 (1976) 399MathSciNetADSCrossRefGoogle Scholar
  31. [21]
    E.Ba Bogolmony, Sov. J. Nucl. Phys. 24 (1976) 449Google Scholar
  32. S. Coleman, S. Parke, A. Neveu and C.M. Sommerfield, Phys. Rev. D15 (1977) 544ADSCrossRefGoogle Scholar
  33. [22]
    C. Montonen and D. Olive, Phys. Lett. 72B (1977) 1 17Google Scholar
  34. [23]
    A. D’Adda, R. Horsley and P. Di Vecchia, Phys. Lett. 76B (1978) 298Google Scholar
  35. [24]
    E. Witten and D. Olive, HUTP 78 IA013 preprint (1978)Google Scholar
  36. [25]
    T. Kaluza, Sitzungber. Prenss. Akad. Wiss. Berlin Math-Phys KA (1921) 1966Google Scholar
  37. O. Klein, Z. Phys. 37 (1926) 895ADSCrossRefGoogle Scholar
  38. W. Thirring, Acta Physica Austriaca, Supp. IX (1972) 266 and references thereinGoogle Scholar
  39. [26]
    S. Coleman and J. Mandula, Phys. Rev. 159 (1967) 1251ADSCrossRefGoogle Scholar
  40. [27]
    For reviews of supersymmetry algebras, see B. Zumino, Proc. 17th Intern. Conf. on High Energy Physics, London 1974 ( Science Research Council, Didcot, 1974 ) p I–254Google Scholar
  41. J. Wess, Lecture Notes in Physics (Springer, Berlin 1974 ) vol. 37, p 352ADSCrossRefGoogle Scholar
  42. L. Corwin, Y. Ne’eman and S. Sternberg, Rev. Mod. Phys. 47 (1975) 573MathSciNetADSMATHCrossRefGoogle Scholar
  43. A. Salam and J. Strathdee, Phys. Rev. Dil (1975) 521Google Scholar
  44. L. 0’Raifertaigh, Comm. Dublin Inst, for Advanced Studies, Series A, Theor. Phys. Nr 22 (1975)Google Scholar
  45. B. Zumino, Proc. Conf. on Gauge Theories and Modern Field Theory, Boston 1975 (MIT press, Cambridge, Mass 1976 ) p 255Google Scholar
  46. A. Salam and J. Strathdee, ICTP preprint, IC176122 (1976)Google Scholar
  47. S. Ferrara, Rivista Nuovo Cimento 6 (1976) 105MathSciNetADSCrossRefGoogle Scholar
  48. P. Fayet and S. Ferrara, Phys. Rep. 32 (1977) 251MathSciNetADSCrossRefGoogle Scholar
  49. S. Ferrara, CERN preprint TH 2514 ( 1978Google Scholar
  50. [28]
    J. Tits, Tabellen zu den Einfachen Lie Gruppen und chre Darstellungen, Lecture Notes in Mathematics 40 (Springer 1967 )Google Scholar
  51. [29]
    See S.W. Hawking, Cargèse Lecture Notes (1978)Google Scholar
  52. [30]
    M.F. Sohnius, Nucl. Phys. B138 (1978) 109MathSciNetADSCrossRefGoogle Scholar
  53. [31]
    D. Olive, private communication (unpublished)Google Scholar
  54. [32]
    W. Nahm, Nucl. Phys. B135 (1978) 149ADSCrossRefGoogle Scholar
  55. [33]
    D.R.T. Jones, Phys. Letters 72B (1977) 199ADSGoogle Scholar
  56. E.C. Poggio and H.N. Pendleton, Phys. Lett. 72B (1977) 200Google Scholar
  57. [34]
    E. Cremmer, B. Julia and J. Scherk, Phys. Lett. 76B (1978) 409Google Scholar
  58. [35]
    R. Haag, J.T. Lopuszanski and M. Sohnius, Nucl. Phys. B88 (1975) 257MathSciNetADSCrossRefGoogle Scholar
  59. [36]
    D.Z. Freedman and J.H. Schwarz, Nucl. Phys. B137 (1978) 333ADSCrossRefGoogle Scholar
  60. [37]
    S. Ferrara and P. Van Nieuwenhuizen, Phys. Lett. 74B (1978) 333Google Scholar
  61. K.S. Stella and P.C. West, Phys. Lett. 74B (1978) 330Google Scholar
  62. S. Ferrara and P. Van Nieuwenhuizen, CERN preprint TH 2484 (1978) to be published in Phys. Lett. B, Ecole Normale Sup. Report LPTENS 78 /14 (1978)Google Scholar
  63. [38]
    A. Salam and J. Strathdee, Nucl. Phys. B76 (1974) 477MathSciNetADSCrossRefGoogle Scholar
  64. S. Ferrara, J. Wess and B. Zumino, Phys. Lett. B51 (1974) 239Google Scholar
  65. J. Wess and B. Zumino, Phys. Lett. 66B (1977) 361MathSciNetGoogle Scholar
  66. R. Grimm, J. Wess and B. Zumino, Phys. Lett. 74B (1978) 51Google Scholar
  67. L. Brink, M. Gell-Mann, P. Ramond and J.H. Schwarz, Phys. Lett. 74B (1978) 336 and Caltech report 68 - 649 (1978)Google Scholar
  68. [39]
    S.W. Mac Dowell and F. Mansouri, Phys. Rev. Lett. 38 (1977) 739MathSciNetADSCrossRefGoogle Scholar
  69. P.K. Townsend and P. Van Nieuwenhuizen, Phys. Lett. B67 (1977)439Google Scholar
  70. Y Ne’mann andT. Regge, Phys. Lett. B76 (1978) 54MathSciNetGoogle Scholar
  71. [40]
    S. Ferrara, F. Gliozzi, J. Scherk and P. Van Nieuwenhuizen, Nucl. Phys. B117 (1976) 333ADSCrossRefGoogle Scholar
  72. [41]
    S. Ferrara, J. Scherk and P. Van Nieuwenhuizen, Phys.Rev. Lett. 37 (1976) 1035MathSciNetADSCrossRefGoogle Scholar
  73. [42]
    E. Cremmer, B. Julia, J. Scherk, P. Van Nieuwenhuizen, S. Ferrara and L. Girardello, Ecole Normale Supérieure preprint 78 /17 (1978)Google Scholar
  74. [43]
    D.Z. Freedman and P. Van Nieuwenhuizen, Phys. Rev. D, Vol. 14 (1976) 912MathSciNetADSCrossRefGoogle Scholar
  75. [44]
    P. Fayet, Nucl. Phys. B1 13 (1976) 135MathSciNetADSCrossRefGoogle Scholar
  76. [45]
    N.S. Manton, Nucl. Phys. B126 (1977) 525MathSciNetADSCrossRefGoogle Scholar
  77. [46]
    M. Gell-Mann, invited paper at the Washington Meeting of Amer.Phys. Soc. April 1977, to be publishedGoogle Scholar
  78. [47]
    K.S. Stelle, Phys. Rev. D, Vol. 16, 4 (1977) 953MathSciNetADSGoogle Scholar
  79. [48]
    J. Scherk and J.H. Sehwarz, Nucl. Phys. B81 (1974) 118, Phys. Lett. 57B (1975) 463Google Scholar
  80. T. Yoneya, Nuovo Cimento Lett. 8 (1973) 951; Prog, of Theor. Phys. Vol. 51 (1974) 1907Google Scholar
  81. J.H. Schwarz, CALT preprint 68–637 (1978) talk presented at Orbis Scientiae 1978, and to be publishedGoogle Scholar
  82. [49]
    The 0(8) theory has been 0recently obtained by dimensional reduction for the D = 11 supergravity theory by E. Cremmer and B. Julia LPTENS 78/23 preprint (1978)Google Scholar

Copyright information

© Plenum Press, New York 1979

Authors and Affiliations

  • J. Scherk
    • 1
  1. 1.Laboratoire de Physique Théorique de l’Ecole Normale Supérieure - 24Paris Cedex 05France

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