Advertisement

Conformal Field Theory at C=1

  • Robbert Dijkgraaf
  • Erik Verlinde
  • Herman Verlinde
Part of the NATO ASI Series book series (NSSB, volume 185)

Abstract

Conformal field theory [1] is a subject of great interest to various disciplines in physics. Although we are still far from a complete understanding, partial results seem to indicate that a beautiful, deep mathematical structure lies at its roots. The situation for central charge c<1 is by now very well understood [2]. The case c=1 however forms in many aspects a natural boundary. Here we meet the new features of an infinity of primary fields and the existence of marginal operators and deformations. Futhermore, the c=1 models allow a natural interpretation as a string complication. As such they can serve as an instructive example of what is to be expected at higher c values.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    A.A. Belavin, A.M. Polyakov and A.B. Zamolodchikov, Nucl. Phys. B241 (1984) 333.MathSciNetADSCrossRefGoogle Scholar
  2. [2a]
    D. Friedan, Z. Qiu and S. Shenker, Phys. Rev. Lett. 52 (1984) 1575.MathSciNetADSCrossRefGoogle Scholar
  3. [2b]
    J.L. Cardy, Nucl. Phys. B270 [FS16] (1986) 186.MathSciNetADSCrossRefGoogle Scholar
  4. [2b]
    D. Gepner, Nucl. Phys. B287 (1987) 111.MathSciNetADSCrossRefGoogle Scholar
  5. [2c]
    A. Capelli, C. Itzykson and J.B. Zuber, Nucl. Phys. B275 [FS17] (1987) 445.ADSCrossRefGoogle Scholar
  6. [3a]
    L. Dixon, J.A. Harvey, C. Vafa and E. Witten, Nucl. Phys. B261 (1985) 620.MathSciNetGoogle Scholar
  7. [3b]
    L. Dixon, J.A. Harvey, C. Vafa and E. Witten, Nucl. Phys. B274 (1986) 285.MathSciNetADSCrossRefGoogle Scholar
  8. [4]
    L. Dixon, D. Friedan, E. Martinec and S. Shenker, Nucl. Phys. B282 (1987) 13.MathSciNetADSCrossRefGoogle Scholar
  9. [5]
    S. Elitzur, E. Gross, E. Rabinovici and N. Seiberg, Nucl. Phys. B283 (1987) 431.Google Scholar
  10. [6]
    P. Di Francesco, H. Saleur and J.B. Zuber, Nucl. Phys. B285 [FS19] (1987) 454.ADSCrossRefGoogle Scholar
  11. [7]
    R. Dijkgraaf, E. Verlinde and H. Verlinde, C=1 Conformal Field Theories on Riemann Surfaces, Utrecht preprint, THU-87/17.Google Scholar
  12. [8]
    P. Ginsparg, Curiosities at c=l, Harvard preprint, HUTP-87/A068.Google Scholar
  13. [9]
    K. Bardacki, E. Rabinovici and B. Spring, String models with c < 1 components, preprint CERN-TH 4760/87.Google Scholar
  14. [10a]
    L.P. Kadanoff, Ann. Phys. 120 (1979) 39.ADSCrossRefGoogle Scholar
  15. [10b]
    L.P. Kadanoff and A.C. Brown, Ann. Phys. 121 (1979) 318.ADSCrossRefGoogle Scholar
  16. [11]
    E. Verlinde, unpublished.Google Scholar
  17. [12]
    J. Harvey, G. Moore and C. Vafa, Quasicrystalline Compactification, Harvard preprint, HUTP-87/A072.Google Scholar
  18. [13]
    J.-P. Serre, Lecture Notes in Mathematics 672 (Springer, 1977), 29-68.Google Scholar
  19. [14a]
    L. Alvarez-Gaumé, G. Moore and C. Vafa, Comm. Math. Phys. 106 (1986) 1.MathSciNetADSMATHCrossRefGoogle Scholar
  20. [14b]
    L. Alvarez-Gaumé, J.B. Bost, G. Moore, P. Nelson and C. Vafa, Phys. Lett. B178 (1986) 41.ADSGoogle Scholar
  21. [14c]
    L. Alvarez-Gaumé, J.B. Bost, G. Moore, P. Nelson and C. Vafa, Comm. Math. Phys. 112 (1987) 503.MathSciNetADSMATHCrossRefGoogle Scholar
  22. [14d]
    E. Verlinde and H. Verlinde, Nucl. Phys. B288 (1987) 357.MathSciNetADSCrossRefGoogle Scholar
  23. [15]
    D. Friedan and S. Shenker, Nucl. Phys. B281 (1987) 509.MathSciNetADSCrossRefGoogle Scholar
  24. [16]
    J. Fay, Theta functions on Riemann surfaces, Springer Notes in Mathematics 352 (Springer, 1973).Google Scholar
  25. [17]
    S. Hamidi and C. Vafa, Nucl. Phys. B279 (1987) 465.MathSciNetADSCrossRefGoogle Scholar
  26. [18]
    K. Miki, Phys. Lett. 191B (1987) 127. D. Bernard, Z-twisted fields and bosonization on Riemann surfaces, Meudon preprint 1987.Google Scholar
  27. [19a]
    N. Ishibashi, Y. Matsuo and H. Ooguri, Tokyo preprint, UT-499, 1986.Google Scholar
  28. [19b]
    L. Alvarez-Gaumé, C. Gomez and C. Reina, Phys. Lett. 190B (1987) 55.ADSGoogle Scholar
  29. [19c]
    New methods in string theory, preprint CERN TH-4775/87. C. Vafa, Phys. Lett. 190B (1987) 47.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Robbert Dijkgraaf
    • 1
  • Erik Verlinde
    • 1
  • Herman Verlinde
    • 1
  1. 1.Institute for Theoretical PhysicsUtrechtThe Netherlands

Personalised recommendations