The Polyakov Approach and Divergences in Open Superstrings

  • C. P. Burgess†
Part of the NATO Science Series book series (NSSB, volume 160)

Abstract

String theories have, recently re-emerged, pheonix-like, into the mainstream of particle physics. The principal reasons for this revival are threefold:
  1. i)

    Superstrings are believed to be renormalizable (possibly even finite), unitary, theories that include gravity as well as the usual gauge and matter interactions [1,2,30,33,34].

     
  2. ii)

    Strings ‘miraculously’ satisfy very stringent requirements of mathematical consistency [2,3,4]. These requirements arise in the form of anomaly-cancellation conditions and are sufficiently restrictive that only a handful (Type I, Types IIa, IIb, and heterotic with gauge groups E8 x E8 or Spin(32)/Z 2) of candidate string theories survive.

     
  3. iii)

    Finally, the Type I and heterotic strings appear to have the potential of producing a realistic phenomenology at energies low enough (i. e. E “ Mp) to be accessible to experiment [5]. (For a review see L. Ibáñez, this volume.)

     

Keywords

Gauge Group Gauge Boson Vertex Operator Spin Structure Heterotic String 
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).
    M.B. Green and J.H. Schwarz, Nucl. Phys. B181(1976) 502; B198(1982) 252; B198(1982) 441; and Phys. Lett. 109B(1982) 444; M.B. Green, J.H. Schwarz, and L. Brink, Nucl. Phys. B198(1982) 474; E. Martinec, Phys. Lett. 171B(1986) 189. ADSGoogle Scholar
  2. 2).
    D.J. Gross, J. Harvey, E. Martinec, and R. Rohm, Phys. Rev. Lett. 54(1984) 502; Nucl. Phys. B256(1985) 253; and Nucl. Phys. B267(1986) 75. MathSciNetADSCrossRefGoogle Scholar
  3. 3).
    E. Witten, in “Geometry, Anomalies and Topology”, edited by W.A. Bardeen and A.R. White, World Scientific (1985).Google Scholar
  4. 4.
    P. Candelas, G.J. Horowitz, A. Strominger and E. Witten, Nucl. Phys. B258 (1985) 46.MathSciNetADSCrossRefGoogle Scholar
  5. 5).
    E. Witten, “Interacting Field Theory of Open Superstrings” Princeton preprint (1986); Nucl. Phys. B268(1986) 253; T. Yoneya, to appear in the proceedings of the 7th Workshop on Grand Unification, Toyama, Japan (1986); H. Hata, K. Itoh, T. Kugo, H. Kunitomo and K. Ogawa, Kyoto preprints; Phys. Lett. 175B(1986) 138; Phys. Lett. 172B(1986) 186, 195; A. Neveu and P.C. West, Phys. Lett. 168B(1986) 192; S.P. de Alwis and N. Ohta, Phys. Lett. 174B(1986) 383; N.P. Chang, H.Y. Guo, Z. Qiu and K. Wu, CCNY-HEP 86/5 (1986); A. Jevicki, Phys. Lett. 169B(1986) 359; J. Lykken and S. Raby, LA-UR-1334 (1986). Google Scholar
  6. 6).
    M.B. Green and J.H. Schwarz, Nucl. Phys. B218 (1983) 43; Nucl. Phys. B243 (1984) 285; M.B. Green, J.H. Schwarz and L. Brink, Nucl. Phys. B219 (1983) 437. MathSciNetADSCrossRefGoogle Scholar
  7. 7).
    P. Ramond, Phys. Rev. D3 (1971) 2415; A. Neveu and J.H. Schwarz, Nucl. Phys. B31 (1971) 86; Phys. Rev. D4 (1971) 1109; J.-L. Gervais and B. Sakita, Nucl. Phys. B34 (1971) 477. MathSciNetADSGoogle Scholar
  8. 8.
    A.M. Polyakov, Phys. Lett. 103B (1981) 207, 211.MathSciNetADSGoogle Scholar
  9. 9).
    D.B. Fairlie and H.B. Nielsen, Nucl. Phys. B20 (1970) 637; C.S. Howe, B. Sakita, and M.A. Virasoro, Phys. Rev. D2 (1970) 2857; O. Alvarez, Nucl. Phys. B216 (1983) 125; D. Freidan, E. Martinec and S. Shenker, Nucl. Phys. B271 (1986) 93. ADSCrossRefGoogle Scholar
  10. 10.
    S. Weinberg, Phys. Lett. 156B(1985), 309.ADSGoogle Scholar
  11. 11).
    E.S. Fradkin and A.A. Tseytlin, Phys. Lett. 158B (1985) 316; Phys. Lett. 160B. 69; and Nucl. Phys. B261 (1985) 1; C.G. Callan, E.J. Martinec and M.J. Perry, Nucl. Phys. B262 (1985) 593; C.G. Callan, I. R. Kebanov, and M.J. Perry, “String Theory Effective Actions” Princeton preprint (1986); B.E. Fridling and A. Jevicki, Phys. Lett. 174B (1986) 75; C.M. Hull and E. Witten, Phys. Lett. 160B (1985) 398; A. Sen, SLAC-PUB-3794 (1985); S.P. de Alwis, Texas preprint UTTG-15–86 (1986). MathSciNetADSGoogle Scholar
  12. 12).
    C.P. Burgess and T.R. Morris, “Open and Unoriented Strings à la Polyakov”, I.A.S. preprint (1986). Google Scholar
  13. 13).
    C.P. Burgess and T.R. Morris, “Open Superstrings à la Polyakov”, I.A.S. preprint(1986). Google Scholar
  14. 14).
    M. Schiffer and D.C. Spencer, “Functionals of Finite Riemann Surfaces” Princeton University Press (1954). MATHGoogle Scholar
  15. 15.
    E. del Guidice, P. DiVecchia and S. Fubini, Ann. Phys. 70 (1972) 378.ADSCrossRefGoogle Scholar
  16. 16).
    J. Pat on and H.M.Chan, Nucl. Phys. B10(1969) 519. ADSGoogle Scholar
  17. 17).
    J.H. Schwarz, in the proceedings of the Johns Hopkins Workshop, (1982); N. Marcus and A. Sagnotti, Phys. Lett. 119B (1982) 97.Google Scholar
  18. 18).
    S. de Alwis, Phys. Lett. 168B(1986) 59; C.G. Callan and Z. Gan, Nucl. Phys. B272(1986) 647. ADSGoogle Scholar
  19. 19).
    O. Alvarez, Nucl. Phys. B216(1983) 125; and in the proceedings of the Work-shop on Unified String Theories, Santa Barbara (1985). ADSCrossRefGoogle Scholar
  20. 20).
    L. Brink, P. DiVecchia and P. Howe, Phys. Lett. 65B(1976) 471; S. Deser and B. Zumino, Phys. Lett. 65B(1976) 369. ADSGoogle Scholar
  21. 21.
    J.H. Schwarz, Phys. Rep. 89C (1982) 223.ADSCrossRefGoogle Scholar
  22. 22).
    N. Seiberg and E. Witten, “Spin Structures in String Theory” Princeton-IAS preprint, (1986). Google Scholar
  23. 23).
    D. Friedan, S. Shenker and E. Martinec, Phys. Lett. 160B(1985) 55; J. Cohn, D. Friedan, Z. Qiu and S. Shenker, Chicago preprint EFI 85-90-Rev. (1986). MathSciNetADSGoogle Scholar
  24. 24).
    G. Moore, P. Nelson and J. Polchinski, Phys. Lett. 169B (1986) 47; E.D’ Hoker and D.H. Phong, Columbia preprint CU-TP-340 (1986)MathSciNetADSGoogle Scholar
  25. 25.
    E. Witten, Comm. Math. Phys. 100 (1985) 197.MathSciNetADSMATHCrossRefGoogle Scholar
  26. 26).
    F. Gliozzi, J. Scherk and D.I. Olive, Phys. Lett. 65B(1976) 282; Nucl. Phys. B122(1977) 253. ADSGoogle Scholar
  27. 27).
    S. Weinberg, Texas preprint UTTG-22-85 (1985). Google Scholar
  28. 28).
    C.P. Burgess, “Finiteness and the Type I Superstring”, IAS preprint (1986). Google Scholar
  29. 29.
    M.B. Green and J.H. Schwarz, Phys. Lett. 151B (1985) 21.MathSciNetADSGoogle Scholar
  30. 30).
    J.Polchinski, Comm. Math. Phys. 104 (1986) 37; E. D’Hoker and D.H.Phong, Nucl. Phys. B269 (1986) 205; E.D’ Hoker and D.H.Phong, Columbia preprint CU-TP-340 (1986). MathSciNetADSMATHCrossRefGoogle Scholar
  31. 31.
    J. Shapiro, Phys. Rev. D5 (1972) 1945.ADSGoogle Scholar
  32. 32).
    H. Yamamoto, Y. Nagahami and N. Nakazawa, Hiroshima preprint RRK 86–20; P.H. Frampton, P. Moxhay, Y.J. Ng, North Carolina preprint IFP-256-UNC (1986); R. Potting and J. Shapiro, (to appear) Phys. Rev. D;L. Clavelli, (to appear) Phys. Rev. D.Google Scholar
  33. 33).
    P.H. Frampton, P. Moxhay, Y.J. Ng, Phys. Rev. Lett. 55(1985) 2107; L. Clavelli, Phys. Rev. D33(1986) 1098. ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1987

Authors and Affiliations

  • C. P. Burgess†
    • 1
  1. 1.Institute for Advanced StudyPrincetonUSA

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