Superstrings and Quark-Lepton Physics

  • Rabindra N. Mohapatra
Part of the Graduate Texts in Contemporary Physics book series (GTCP)


In this chapter, we wish to explore the consequences of the hypothesis that as one probes very small distances (l≤10-33 cm), the fundamental particles may exhibit a stringlike structure with a size of the order of the Planck size (i.e., 10-33 cm), thereby departing from the point particle assumption made throughout the rest of the book. Historically, strings were introduced [1] to describe the world of hadrons, but the appearance of spin 2 particles in the string spectrum, as well as other problems, prompted J. Scherk and J. Schwarz to suggest that they may be relevant for the description of a unified theory of gravity and elementary particles. It is this idea which has been developed into the beautiful superstring theories, which some believe could represent the ultimate theory of everything.


Gauge Group Yukawa Coupling Euler Characteristic Chern Class Betti Number 
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  1. [1]
    For a complete survey of the developments up to 1986, seeGoogle Scholar
  2. M. Green, J. H. Schwarz, and E. Witten, Superstring Theories, vols. I and II, Cambridge University Press, Cambridge, 1986;Google Scholar
  3. M. Kaku, Introduction to Superstrings, Springer-Verlag, New York, 1988.zbMATHCrossRefGoogle Scholar
  4. [2]
    Y. Nambu, in Symmetries and Quark Model (edited by R. Chand ), Gordon and Breach, New York, 1970, p. 269;Google Scholar
  5. T. Goto, Prog. Theor. Phys. 46, 1560 (1971).MathSciNetADSzbMATHCrossRefGoogle Scholar
  6. [3]
    A Neveu and J. Schwarz, Nucl. Phys. B31, 86 (1971);ADSCrossRefGoogle Scholar
  7. P. Ramond, Phys Rev. D3, 2415 (1971).MathSciNetADSGoogle Scholar
  8. [4]
    F. Gliozzi, J. Scherk, and D. Olive, Phys. Lett. 65B, 282 (1976); Nucl. Phys. B22, 253 (1977).Google Scholar
  9. [5]
    D. Gross, J. Harvey, E. Martinec, and R. Rohm, Nucl. Phys. B256, 253 (1985).MathSciNetADSCrossRefGoogle Scholar
  10. [6]
    For a thorough discussion of higher dimensional theories, seeGoogle Scholar
  11. T. Appelquist, A. Chodos, and P. Freund, Modern Kaluza—Klein Theories, Benjamin-Cumings, New York, 1988.Google Scholar
  12. [7]
    S. Coleman, Phys. Rev. D11, 2088 (1975).ADSGoogle Scholar
  13. [8]
    S. Mandelstam, Phys. Rev. D11, 3026 (1975).MathSciNetADSGoogle Scholar
  14. [9]
    E. Bergshoeff, M. de Roo, B. de Wit, and P. van Nieuenhuizen, Nucl. Phys. B195, 97 (1982).ADSCrossRefGoogle Scholar
  15. [10]
    G. Chapline and N. S. Manton, Phys. Lett. 120B, 105 (1983).MathSciNetGoogle Scholar
  16. [11]
    M. B. Green and J. H. Schwarz, Phys. Lett. 149B, 117 (1982).Google Scholar
  17. [12]
    P. Candelas, G. Horowitz, A. Strominger, and E. Witten, Nucl. Phys. B258, 46 (1985).MathSciNetADSCrossRefGoogle Scholar
  18. [13]
    An excellent review of differential geometry relevant to our discussion can be found in [1] as well asGoogle Scholar
  19. T. Eguchi, R. Gilkey, and A. Hanson, Phys. Rep. 66, 213 (1980).MathSciNetADSCrossRefGoogle Scholar
  20. [14]
    T. Hübsch, Comm. Math. Phys. 108, 291 (1987);MathSciNetADSzbMATHCrossRefGoogle Scholar
  21. see also T. Hübsch, University of Maryland Ph.D. Thesis (1987).Google Scholar
  22. [15]
    G. Tian and S. T. Yau, Proceedings of the Argonne Symposium on “Anomalies, Geometry and Topology” (edited by W. Bardeen et al.), World Scientific, Singapore, 1985.Google Scholar
  23. [16]
    K. Kodaira, Complex Manifolds and Deformations of Complex Structures, Springer-Verlag, New York, 1985.Google Scholar
  24. [17]
    B. Greene, K. Kirklin, P. Miron, and G. G. Ross, Nucl. Phys. B278, 667 (1986).MathSciNetADSCrossRefGoogle Scholar
  25. [18]
    For consideration of E6-GUT, seeGoogle Scholar
  26. F. Gursey, P. Sikivie, and P. Ramond, Phys. Lett. 60B, 177 (1976);Google Scholar
  27. F. Gursey and M. Serdaroglue, Nuovo Cimento 65A, 337 (1981);ADSCrossRefGoogle Scholar
  28. Y. Achiman and B. Stech, Phys. Lett. 77B, 389 (1978).Google Scholar
  29. [19]
    R. Aspinwall, B. Greene, K. Kirklin, and P. Miron, Nucl. Phys. B294, 1983 (1987);MathSciNetCrossRefGoogle Scholar
  30. P. Candelas, A. Dale, C. Lutken, and R. Schimmrigk, Nucl. Phys. B298, 493 (1988).MathSciNetADSCrossRefGoogle Scholar
  31. [20]
    Y. Hosotani, Phys. Lett. 126B, 303 (1983).Google Scholar
  32. [21]
    E. Witten, Nucl. Phys. B258, 75 (1985);MathSciNetADSCrossRefGoogle Scholar
  33. G. Segre, “Schladming Lectures” (1986) for a review; A. Sen, Phys. Rev. Lett. 55, 33 (1985).ADSCrossRefGoogle Scholar
  34. [22]
    M. Dine, V. Kaplunovsky, M. Mangano, C. Nappi, and N. Seiberg, Nucl. Phys. B259, 519 (1985).MathSciNetADSCrossRefGoogle Scholar
  35. [23]
    R. N. Mohapatra, Phys. Rev. Lett. 56, 561 (1986);ADSCrossRefGoogle Scholar
  36. R. N. Mohapatra and J. W. F. Valle, Phys. Rev. D34, 1642 (1986).MathSciNetADSCrossRefGoogle Scholar
  37. [24]
    J. P. Deredinger, L. Ibanez, and H. P. Nilles, Nucl. Phys. B267, 365 (1986);ADSCrossRefGoogle Scholar
  38. S. Nandi and U. Sarkar, Phys. Rev. Lett. 56, 564 (1986).ADSCrossRefGoogle Scholar
  39. For other solutions to the neutrino mass problem, seeGoogle Scholar
  40. A. Masiero, D. Nanopoulos, and A. Sanda, Phys. Rev. Leu. 57, 663 (1986); E. Ma, Phys. Rev. Lett. 58, 969 (1987).CrossRefGoogle Scholar
  41. [25]
    M. Bento, L. Hall, and G. G. Ross, Nucl. Phys. B292, 400 (1987).ADSCrossRefGoogle Scholar
  42. [26]
    M. Dine, N. Seiberg, X. Wen, and E. Witten, Nucl. Phys. B278, 769 (1986).MathSciNetADSCrossRefGoogle Scholar
  43. [27]
    M. Cvetiè, Phys. Rev. Lett. 59, 1795 (1987).MathSciNetADSCrossRefGoogle Scholar
  44. [28]
    J. Ellis, K. Enquist, D. Nanopoulos, and K. Olive, Phys. Lett. 188B, 415 (1987);Google Scholar
  45. G. Costa, F. Feruglio, F. Gabbiani, and F. Zwirner, Nucl. Phys. B286, 325 (1986).ADSCrossRefGoogle Scholar
  46. [29]
    J. P. Deredinger et al,ref. [24];Google Scholar
  47. M. Dine, N. Seiberg, R. Rohm, and E. Witten, Phys. Lett. 156B, 55 (1985).MathSciNetGoogle Scholar
  48. [30]
    J. Breit, B. Ovrut, and G. Segre, Phys. Lett. 162B, 303 (1985)Google Scholar
  49. P. Binetruy and M. K. Gaillard, Phys. Lett. 168B, 347 (1986)Google Scholar
  50. J. Ellis. C. Gomez, and D. V. Nanopoulos, Phys. Lett. 171B, 302 (1986)MathSciNetGoogle Scholar
  51. M. Quiros, Phys. Lett. 173B, 265 (1986)MathSciNetGoogle Scholar
  52. Y. J. Ahn and J. Breit, Nucl. Phys. B273, 253 (1986)ADSCrossRefGoogle Scholar
  53. P. Binetruy, S. Dawson, and I. Hinchliffe, Phys. Lett. 179B, 262 (1986)Google Scholar
  54. [31]
    J. Ellis, C. Kounras, and D. Nanopoulos, Nucl. Phys. B241, 406 (1984); Nucl. Phys. B247, 373 (1984);ADSCrossRefGoogle Scholar
  55. N. Chang, S. Ouvry, and X. Wu, Phys. Rev. Lett. 5, 327 (1983).ADSCrossRefGoogle Scholar
  56. [32]
    K. Yamamoto, Phys. Lett. B168, 341 (1986).Google Scholar
  57. [33]
    G. Lazaridis, C. Panagiotakopoulos, and Q. Shafi, Phys. Rev. Lett. 56, 557 (1986).ADSCrossRefGoogle Scholar
  58. [34]
    R. N. Mohapatra and J. W. F. Valle, Phys. Lett. B186, 303 (1987).Google Scholar
  59. [35]
    K. Yamamoto, Phys. Lett. B194, 390 (1987).Google Scholar
  60. [36]
    S. Kalara and R. N. Mohapatra, Phys. Rev. D35, 3143 (1987).MathSciNetGoogle Scholar
  61. [37]
    S. Kalara and R. N. Mohapatra, Z. Phys. C37, 395 (1988);Google Scholar
  62. see also F. del Aguila, M. Daniel, M. Blair, and G. G. Ross, Nucl. Phys. B272, 413 (1986).ADSCrossRefGoogle Scholar
  63. [38]
    M. Matsuda, T. Matsuoka, H. Mino, D. Suematsu, and Y. Yamada, Prog. Theor. Phys. 79, 174 (1988).ADSCrossRefGoogle Scholar
  64. [39]
    P. Candelas, Nucl. Phys. B298, 458 (1988).MathSciNetADSCrossRefGoogle Scholar
  65. [40]
    G. Tian and S. T. Yau, Proceedings of the Symposium on “Anomalies, Geometry and Topology” (edited by W. A. Bardeen and A. R. White ), World Scientific, Singapore, 1985.Google Scholar
  66. [41]
    B. R. Greene, K. Kirklin, P. Miron, and G. G. Ross, Nucl. Phys. B278, 667 (1986); Phys. Lett. 180B, 69 (1986); Nucl. Phys. B292, 606 (1987).MathSciNetADSCrossRefGoogle Scholar
  67. [42]
    S. Kalara and R. N. Mohapatra, Phys. Rev. D36, 3474 (1987);MathSciNetADSGoogle Scholar
  68. S. Kalara, P. K. Mohapatra, and R. N. Mohapatra, Phys. Rev. D37, 3284 (1988);ADSGoogle Scholar
  69. P. Candelas and S. Kalara, Nucl. Phys. B298, 357 (1988).MathSciNetADSCrossRefGoogle Scholar
  70. [43]
    P. S. Aspinwall, B. Greene, K. Kirklin, and P. Miron, Nucl. Phys. B294, 193 (1987).MathSciNetADSCrossRefGoogle Scholar
  71. [44]
    P. Candelas, A. M. Dale, C. A. Lötken, and R. Schimmrigk, Nucl. Phys. B298, 493 (1988).ADSCrossRefGoogle Scholar
  72. [45]
    G. Lazaridis and Q. Shafi, J. Math. Phys. 36, 711 (1989).ADSCrossRefGoogle Scholar
  73. [46]
    E. Rusjan and G. Senjanovic, VPI preprint (1988).Google Scholar
  74. [47]
    C. Panagiotakopoulos, CERN-T-5447/89;Google Scholar
  75. R. Arnowitt and P. Nath, Phys. Rev. 62, 222 (1989); Phys. Rev. D39, 2006 (1989);Google Scholar
  76. F. del Aguila, G. Coughlan, and M. Masip, Nucl. Phys. B351 90 (1991); F. del Aguila, G. Coughlan, and L. da Mota, UGPT-7–91.Google Scholar
  77. [48]
    R. N. Mohapatra, E. Rusjan, A. Sokorac, and G. Senjanovic, Phys. Lett. 225B, 85 (1989).MathSciNetGoogle Scholar
  78. [49]
    M. Dine and N. Seiberg, Phys Lett. 162B, 299 (1985);MathSciNetGoogle Scholar
  79. V. Kaplunovsky, Phys. Rev. Lett. 55, 1036 (1985).ADSCrossRefGoogle Scholar
  80. [50]
    M. Cvetic, Phys. Rev. Lett. 59, 1795 (1987).MathSciNetADSCrossRefGoogle Scholar
  81. [51]
    For a recent overview of the situation, seeGoogle Scholar
  82. M. Dine and C. Lee, Institute for Advanced Study, preprint (1988).Google Scholar
  83. [52]
    D. Gepner, Nucl. Phys. B296, 757 (1988); Phys. Lett. B199, 380 (1987).MathSciNetGoogle Scholar
  84. [53]
    For some attempts in this direction, seeGoogle Scholar
  85. J. Distler and B. Greene, Nucl. Phys. B309, 295 (1988).MathSciNetADSCrossRefGoogle Scholar
  86. [54]
    L. Dixon, J. Harvey, C. Vafa and E. Witten, Nucl. Phys. B261, 678 (1985); Nucl. Phys. B274, 285 (1986);MathSciNetGoogle Scholar
  87. K. S. Narain, Phys. Lett. B169, 41 (1986);MathSciNetGoogle Scholar
  88. W. Lerche, D. Lust, and A. Schellekens, Nucl. Phys. B287, 447 (1987).ADSCrossRefGoogle Scholar
  89. [55]
    L. E. Ibanez, H. P. Nilles, and F. Quevedo, Phys. Lett. B187, 25 (1987); B192, 332 (1987).MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Rabindra N. Mohapatra
    • 1
  1. 1.Department of Physics and AstronomyUniversity of MarylandCollege ParkUSA

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