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Spontaneously Generated Field Theories, Zero-Center Modules, Colored Singletons and the Virtues of N = 6 Supergravity

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Book cover Essays on Supersymmetry

Part of the book series: Mathematical Physics Studies ((MPST,volume 8))

Abstract

Attention is called to an interesting property of the space of one-particle states in some especially important massless field theories: the appearance of a one-particle ghost with zero energy. It appears in conformal as well as de Sitter electrodynamics, in the physical sectors of the field mode representations of the respective symmetry groups. It appears again in super de Sitter electrodynamics based on the superalgebra osp(4/l) and in super conformal electrodynamics based on su(2,2/l). We next construct two families of extended super QED, incorporating this property, based on osp(4/N) and on su(2,2/N). There is precisely one osp(4/N) theory and one su(2,2/N) theory of this type for each value of N. The osp(4/6) theory is the same as N = 6 extended supergravity, this is the only one among this family of osp(4/N) theories in which the highest spin is 2. All the one particle states are massless, and in the osp(4/N) theories they can be interpreted as states of two colored singletons. We also critically examine the concept of the Witten index in flat space as well as in de Sitter supersymmetric field theories.

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References

  1. A. D. Sakharov, Dokl. Acad. Nauk SSSR 177, 70 (1967); S. T. Adler, Rev. Mod. Phys. 54, 729 (1982).

    ADS  Google Scholar 

  2. H. Terazawa, Phys. Rev. D 22, 184 (1980); and Refs. 6 and 7.

    ADS  Google Scholar 

  3. N. T. Evans, J. Math. Phys. 8, 170 (1967); C. Fronsdal, Rev. Mod. Phys. 37, 221 (1965).

    Article  ADS  MATH  Google Scholar 

  4. C. Fronsdal, Phys. Rev. D12, 3819 (1975).

    MathSciNet  ADS  Google Scholar 

  5. P. A. M. Dirac, J. Math. Phys. 4, 901 (1963).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. M. Flato and C. Fronsdal, Lett. Math. Phys. 2, 421 (1978).

    Article  MathSciNet  ADS  Google Scholar 

  7. M. Flato and C. Fronsdal, Phys. Lett. 97B. 236 (1980).

    ADS  Google Scholar 

  8. G. Mack, Comm. Math. Phys. 55, 1 (1977).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. G. Mack and I. Todorov, J. Math. Phys. 10, 2078 (1969).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. B. Binegar, C. Fronsdal, and W. Heidenreich, J. Math. Phys. 24, 2828 (1983).

    Article  MathSciNet  ADS  Google Scholar 

  11. G. Rideau, J. Math. Phys. 19, 1627 (1978).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. H. Araki, Comm. Math. Phys. 97, 149 (1985).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. B. Binegar, C. Fronsdal and W. Heidenreich, Ann. Phys. 149, 254 (1982).

    MathSciNet  ADS  Google Scholar 

  14. E. Angelopoulos, M. Flato, C. Fronsdal, and D. Sternheimer, Phys. Rev. D23, 1278 (1981).

    MathSciNet  ADS  Google Scholar 

  15. I. N. Bernshtein, I. M. Gel’fand and S. I. Gel’fand, Funct. Anal. Priozen 5, 1 (1971) [Func. Anal. Appl. 5, 1 (1971)]; G. Pinczon and J. Simon, Rep. Math. Phys. 16, 49 (1979).

    Article  MATH  Google Scholar 

  16. D. Vogan, “Representations of Real Reductive Lie Groups,” Birkhaüser, Boston-Basel-Stuttgart (1981).

    Google Scholar 

  17. G. Zuckerman, Ann. Math . 106, 295 (1977).

    Article  MathSciNet  MATH  Google Scholar 

  18. B. Binegar, “On the Unitarity of Conformal Supergravity,” UCLA/84/TEP/6 preprint, June 1984.

    Google Scholar 

  19. M. Kaku, P. K. Townsend and P. van Nieuwenhuizen, Phys. Lett. 69B, 304 (1977).

    ADS  Google Scholar 

  20. C. Fronsdal, Phys. Rev. D30, 208 (1984).

    MathSciNet  ADS  Google Scholar 

  21. H. Nicolai and E. Sezgin, Nucl. Phys. B242. 69 (1984); L. Castell, W. Heidenreich and T. Künemund, “All Unitary Positive UIRs of osp(N,4),” Starnberg preprint 1984.

    Google Scholar 

  22. G. Rideau, Rep. Math. Phys. 16, 251 (1979).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  23. R. Akhoury and A. Comtet, Nucl. Phys. B246, 253 (1984).

    Article  MathSciNet  ADS  Google Scholar 

  24. E. Witten, Nucl. Phys: B202. 153 (1982).

    MathSciNet  Google Scholar 

  25. J. Fang and C. Fronsdal, Phys. Rev. D22, 1361 (1980).

    MathSciNet  ADS  Google Scholar 

  26. Ref. 13, Appendix.

    Google Scholar 

  27. J.-P. Gazeau, “Gauge Fixing and Gupta-Bleuler Triplets in de Sitter QED,” UCLA/84/TEP/8, July 1984, to appear in J. Math. Phys.

    Article  MathSciNet  Google Scholar 

  28. P. A. M. Dirac, Ann. Math. 37, 429 (1936).

    Article  MathSciNet  Google Scholar 

  29. J. Wess and B. Zumino, Nucl. Phys. B70, 39 (1974).

    Article  MathSciNet  ADS  Google Scholar 

  30. B. W. Keck, J. Phys. A8, 1819 (1975).

    MathSciNet  ADS  Google Scholar 

  31. C. Fronsdal, Lett. Math. Phys. 1 165 (1976).

    Article  MathSciNet  ADS  Google Scholar 

  32. B. Zumino, Nucl. Phys . B127. 189 (1977).

    Article  ADS  Google Scholar 

  33. C. Fronsdal and T. Hirai, “Unitary Representations of Supergroups,” UCLA preprint, April 1985, in this volume.

    Google Scholar 

  34. P. Breitenlohner and D. Z. Freedman, Ann. Phys. 144, 249 (1982).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  35. D. Z. Freedman and H. Nicolai, Nucl. Phys. B237, 342 (1984).

    Article  MathSciNet  ADS  Google Scholar 

  36. S. Ferrara, J. Wess and B. Zumino, Phys. Lett. B51_, 239 (1974).

    ADS  Google Scholar 

  37. N. Bourbaki, “Groupes et Algebres de Lie” (Hermann, Paris 1975) Chapters 4–8.

    MATH  Google Scholar 

  38. V. Bargmann, Comm. Pure Appl. Math. 14, 187 (1961), and ibid. 20, 1 (1967).

    Article  MathSciNet  MATH  Google Scholar 

  39. C. Fronsdal, Phys. Rev. D26, 1988 (1982).

    MathSciNet  ADS  Google Scholar 

  40. M. Günaydin and C. Saclioglu, Phys. Lett. 108B, 169 (1982); M. Günaydin, in “Group Theoretical Methods in Physics,” Istanbul, 1982 (Lecture Notes in Physics 180, Springer-Verlag).

    Google Scholar 

  41. H. Nicolai, “Representations of Supersymmetry in Anti-de Sitter Space,” CERN TH. 3882, April 1984.

    Google Scholar 

  42. M. Flato and C. Fronsdal, Lett. Math. Phys. 8, 159 (1984).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  43. B. Binegar, “Conformal Superalgebras, Massless Representations and Hidden Symmetries,” UCLA/85/TEP/16 preprint, June 1985.

    Google Scholar 

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Authors
  1. M. Flato
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  2. C. Fronsdal
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Editor information

Editors and Affiliations

  1. Department of Physics, UCLA, Los Angeles, USA

    C. Fronsdal

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© 1986 D. Reidel Publishing Company

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Flato, M., Fronsdal, C. (1986). Spontaneously Generated Field Theories, Zero-Center Modules, Colored Singletons and the Virtues of N = 6 Supergravity. In: Fronsdal, C. (eds) Essays on Supersymmetry. Mathematical Physics Studies, vol 8. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4624-8_4

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  • DOI: https://doi.org/10.1007/978-94-009-4624-8_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8555-7

  • Online ISBN: 978-94-009-4624-8

  • eBook Packages: Springer Book Archive

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