Supergravity Grand Unification

  • Pran Nath
  • R. Arnowitt
  • A. H. Chamseddine
Part of the Studies in the Natural Sciences book series (SNS, volume 20)


A review of the recent proposal of Supergravity Grand Unification is given. Topics include the structure of Supergravity GUTS, symmetry breaking through Supergravity induced effects, protection at low energy from intermediate and superheavy mass scales, effective potential and the particle spectrum at low energy. Experimental consequences of Supergravity GUTS and in particular the decays of W and Z into photino, Wino and Zino modes and their branching ratios in various channels are also discussed.


Vector Multiplet Light Field Hide Sector Chiral Multiplet Meson Mass 


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  1. 1.
    A.H. Chamseddine, R. Arnowitt and P. Nath, Phys. Rev. Lett. 49, 970 (1982).CrossRefGoogle Scholar
  2. 2.
    P. Nath, R. Arnowitt and A.H. Chamseddine, Phys. Letters 121B, 33 (1983).Google Scholar
  3. 3.
    R. Arnowitt, A.H. Chamsiddine and P. Nath, Phys. Letters 120B, 145 (1983).Google Scholar
  4. 4.
    L.E. Ibanes, TH, 3374-CERN (1982); Universidad Autonoma de Madrid preprint, FTUAMI 82–8 (1982).Google Scholar
  5. 5.
    R. Barbieri, S. Ferrara and C.A. Savoy, Phys. Lett. 119B, 353 (1982);Google Scholar
  6. H.P. Nilles, M. Srednicki and D. Wyler, TH 3432-CERN (1982).Google Scholar
  7. 6.
    J. Ellis, D.V. Nanopoulos and K. Tamvakis, Phys. Lett. 121B, 1231 (1983);Google Scholar
  8. J. Ellis, J.S. Hagelin, D.V. Nanopoulos and K. Tamvakis, SLAC-POB-3042 (1983).Google Scholar
  9. 7.
    H.P. Nilles, M. Srednicki and D. Wyler, TH. 3461-CERN (1982);Google Scholar
  10. B. Lahanas, TH. 3467-CERN (1982).Google Scholar
  11. 8.
    S. Ferrara, D.V. Nanopoulos and C.A. Savoy, TH. 3442-CERN (1982).Google Scholar
  12. 9a.
    L. Hall, J. Lykken and S. Weinberg, University of Texas Report No. UTTG-1–83.Google Scholar
  13. 9b.
    P. Nath, R. Arnowitt and A.H. Chamseddine, NUB112579 (1982)/ HUTP-82/A057.Google Scholar
  14. 10.
    N. Ohta, Tokyo-Preprint UT-388; C.S. Aulakh, CCNY-HEP-83/2;Google Scholar
  15. J. Leon, M. Quiros and M. Ramon Medrano, Madrid Preprint.Google Scholar
  16. 11.
    L. Alvarez-Gaume, J. Polchinski and M.B. Wise HUTP-821A063/ CALT-68–990.Google Scholar
  17. 12.
    E. Cremmer, P. Fayet and L. Girandello, University of Paris preprint LPTENS-82/30 (1982);Google Scholar
  18. S.K. Soni and H.A. Weldon, University of Pennsylvania preprint (1983).Google Scholar
  19. 13a.
    S. Weinberg, Phys. Rev. Letters 50, 387 (1983).CrossRefGoogle Scholar
  20. 13b.
    R. Arnowitt, A.H. Chamseddine and P. Nath, Phys. Rev. Letters 50, 232 (1983).CrossRefGoogle Scholar
  21. 14.
    E. Witten, Nucl. Phys. B177 (1981); B185, 513 (1981);CrossRefGoogle Scholar
  22. M. Dine, W. Fishier and M. Srednicki, Phys. Lett. 104B, 199 (1981);Google Scholar
  23. S. Dimopoulos and H. Georgi, Nucl. Phys. B193, 150 (1981);CrossRefGoogle Scholar
  24. N. Sakai, Z. für Phys. C11, 153 (1981);CrossRefGoogle Scholar
  25. D.V. Nanopoulos and K. Tamvakis, CERN preprints TH. 3327, 3247 (1982);Google Scholar
  26. R.K. Kaul, Phys. Lett. 109B, 19 (1982);Google Scholar
  27. C.S. Aulakh and R.H. Mohapatra Preprint CCNY-HEP-82/4; C. Nappi and V. Ovrut, Phys. Lett. 113B, 175 (1982);CrossRefGoogle Scholar
  28. L. Alvarez-Gaume, M. Claudson and M.B. Wise, Nucl. Phys. B207, 96 (1982).CrossRefGoogle Scholar
  29. 15.
    For a recent review of globally sypersymmetric theories see P. Fayet, in proceedings of the 21st International Conference on High Energy Physics, Paris 26–31 July 1982, Journal de Physique C3–673.Google Scholar
  30. 16.
    J. Wess and B. Zumino, Nucl. Phys. B70, 39 (1974).CrossRefGoogle Scholar
  31. 17.
    D.Z. Freedman, P. van Nieuwenhuizen and S. Ferrara, Phys. Rev. 1013, 3214 (1976);Google Scholar
  32. S. Deser and B. Zumino, Phys. Lett. 62B, 335 (1976).Google Scholar
  33. 18.
    S. Ferrara and P. van Nieuwenhuizen, Phys. Lett. 76B; J. Stelle and P. West, Phys. Lett. 77B, 376 (1978); 74B, 330 (1978); Nucl. Phys. B145, 175 (1978).Google Scholar
  34. 19.
    We use conventions of P. van Nieuwenhuizen, Phys. Reports 68 (4), 189–398 (1981).Google Scholar
  35. 20.
    E. Cremmer, B. Julia, J. Scherk, S. Ferrara, L. Girardello and P. van Nieuwenhuizen, Nucl. Phys. B147, 105 (1979)CrossRefGoogle Scholar
  36. 21.
    E. Cremmer, S. Ferrara, L. Girardello and A. Van Proeyen, Phys. Lett. 116, B231 (1982) Th. 3348-CERN (1982).Google Scholar
  37. 22.
    J. Bagger and E. Witten, Phys. Lett. 118B, 103 (1982);Google Scholar
  38. J. Bagger, Nucl. Phys. B211, 302 (1983).CrossRefGoogle Scholar
  39. 23.
    (d-1)ba appearing in Eq. (2.11) is the inverse of the matrix d,ab-Google Scholar
  40. 24.
    B. Zumino, Phys. Lett. 87B, 203 (1979).Google Scholar
  41. 25.
    Such a choice is motivated in part by the reasoning that supergravity loop corrections would maintain an approximate U(n) symmetry among its n chiral superfields if the matter couplings are small.9a Thus, one may simulate gravitational quantum loop corrections in scalar potential by choosing a general function of ZaZa+ for d(Z,Z+).Google Scholar
  42. 26.
    In this case, Tab has at least one zero eigenvalue.Google Scholar
  43. 27.
    S. Dimopoulos and S. Raby, Los Alamos Preprint LA-UR-82–1282; J. Ellis, L. Ibanes and G. Ross, Rutherford Preprint RL 82–024 (1982);Google Scholar
  44. J. Polchinsky and L. Susskind, Phys. Rev. D26, 3361 (1982).CrossRefGoogle Scholar
  45. 28.
    S. Weinberg, in General Relativity-An Einstein Centenary Survey, edited by S.W. Hawking and W. Israel ( Cambridge University Press, Cambridge, England, 1979 ), Chapter 16.Google Scholar
  46. 29.
    The simplest super-Higgs potential is a linear one defined by30 g2(Z) = m2(Z+B). The minima correspond to KZ(-1) = a(i2,); KB(-1) = -a(2i - f); a = ±1.Google Scholar
  47. 30.
    J. Polony, University of Budapest Report No. KFKI-1977–93, 1977 (unpublished); See also Ref. 20.Google Scholar
  48. 31.
    Actually one may maintain the desired protection and allow a mixed term in the superpotential e.g., g3(Za,Zs) = al abs ZaZbZs+ a2 ars ZaZrZs if the couplings al abs are 0(Kmg) and X2 ars are 0(K2mg2).Google Scholar
  49. 32.
    There are four mass parameters in the low energy effective potential for the case where one has a general Kühler metric in the original potential.9a Google Scholar
  50. 33.
    The necessity of fine tuning to achieve light Higgs doublets cannot be circumvented in an obvious way in this model. We thank C.S. Aulakh and J. Polchinsky for discussions on this question.Google Scholar
  51. 34.
    It is straightforward to construct global models where the Higgs doublets are naturally light using the “missing partner” mechanism. See in this context, B. Grinstein, Nucl. Phys. B206, 387–396 (1982);Google Scholar
  52. A. Masiero, D.V. Nanopoulos, K. Tamvakis and T. Yanagida, Phys. Lett. 115B, 380 (1982);Google Scholar
  53. H. Georgi, Phys. Lett. 108B, 283 (1982);Google Scholar
  54. S. Dimopoulos and H. Georgi, HUTP-82/A046 (1982).Google Scholar
  55. 35.
    A similar suggestion has also been made by Ferrara et al. in Ref. 8 in the context of the missing partner scenario.34 Google Scholar
  56. 36.
    For this purpose one needs a large mass of the topGoogle Scholar
  57. 37.
    A more general phenomenological analysis which can interpolate between the formalism where spontaneous breaking occurs at the tree level and the one where spontaneous symmetry breaking is triggered through radiative corrections can be given, and shall be presented elsewhere.Google Scholar
  58. 38.
    A model independent prediction of the existence of a Wino below the W meson mass and a Zino below the Z meson mass is given by S. Weinberg.13a Google Scholar
  59. 39.
    For the case of the linear super-Higgs model29 m1 has the value ml = 2 mg(3X - x) where X = a2/a1 and U = - msx/(v2 X3).Google Scholar
  60. 40.
    mH is a model dependent quantity proportional to the gravitino mass and for the linear super-Higgs model it has the value mÌi = mg + (3a - x) 231/2 as discussed in Ref. (13b).Google Scholar
  61. 41.
    For the model of Ref. 29, ß has the value ß = I(-x + 3X - 3 + /). In the more general analysis of Ref. 9a, allowing also for a curved Kahler manifold mv’ need not have the value m.Google Scholar
  62. 42.
    R. Arnowitt, C.H. Chamseddine and P. Nath (unpublished).Google Scholar
  63. 43.
    P. Fayet, Ecole Normale Superiere preprint LPTENS-82/12 (1982); J. Ellis and J.S. Hagelin, SLAC-PUB-3014 (1982).Google Scholar
  64. 44.
    P. Salati and J.C. Wallet, LAPP-TH-65 (1982).Google Scholar
  65. 45.
    R. Brandelik et al., Phys. Lett. 117B, 365 (1982).Google Scholar
  66. 46.
    P. Nath, R. Arnowitt and A.H. Chamseddine, “Wino and Zino Decays of the W and Z Mesons,” NUB2588.Google Scholar
  67. 47.
    There is an additional factor of 4 omitted in Eq. (16) of Ref. 13b and Eq. (47) of Ref. 48.Google Scholar
  68. 48.
    P. Nath, R. Arnowitt and A.H. Cham_seddine, “Global and Local Supersymmetric Grand Unification,” NUB#2586.Google Scholar

Copyright information

© Plenum Press, New York 1985

Authors and Affiliations

  • Pran Nath
    • 1
  • R. Arnowitt
    • 2
  • A. H. Chamseddine
    • 1
  1. 1.Northeastern UniversityBostonUSA
  2. 2.Harvard UniversityCambridgeUSA

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