Toward a Classification of Conformal Field Theories

  • Michio Kaku
Part of the Graduate Texts in Contemporary Physics book series (GTCP)


In order to make some sense out of the jungle of conformal field theories that have been discovered from string theory, physicists have tried to classify these vacuums using various techniques, with varying degrees of success. At present, no comprehensive classification scheme exists that gives us insight into the structure of these vacuums. In fact, it is still largely a mystery why conformal field theories behave as they do. There has been some progress in understanding conformal field theories with finite numbers of primary fields, but there is almost no real understanding of conformal field theories with infinite numbers of primary fields. If a convenient and powerful classification scheme could be devised, then it may be possible to see nontrivial relationships between different conformal field theories, which in turn may help us to understand which, if any, of these conformal field theories have a physical application.


Central Charge Operator Product Expansion Conformal Field Theory Free Field Discrete Subgroup 
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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  1. 1.
    P. Goddard, A. Kent, and D. Olive, Comm. Math. Phys. 103, 105 (1986).MathSciNetADSMATHCrossRefGoogle Scholar
  2. 2.
    B. L. Feigin and D. B. Fuchs, unpublished.Google Scholar
  3. 3.
    VI. S. Dotsenko and V. A. Fateev, Nucl. Phys. B240[FS12], 312 (1984).MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    VI. S. Dotsenko and V. A. Fateev, Nucl. Phys. F251[FS13], 691 (1985).MathSciNetADSCrossRefGoogle Scholar
  5. 5.
    VI. S. Dotsenko, Lectures on Conformal Field Theory, Advances in Studies in Pure Mathematics, vol. 16 (1988).Google Scholar
  6. 6.
    M. A. Bershadsky, V. G. Knizhnik, and M. G. Teitelman, Phys. Lett. 151B, 31 (1984).MathSciNetADSGoogle Scholar
  7. 7.
    J. Bagger, D. Nemeschansky, and J. Zuber, Phys. Lett. 216B, 320 (1989).MathSciNetADSGoogle Scholar
  8. 8.
    N. Ohta and H. Suzuki, Nucl. Phys. B332, 146 (1990).MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    M. Kuwahara, N. Ohta, and H. Suzuki, Phys. Lett. 235B, 57 (1989).MathSciNetADSGoogle Scholar
  10. 10.
    A. B. Zamolodchikov, JETP Lett. 43, 731 (1986); Soviet J. Nucl. Phys. 46, 1090 (1987); Soviet J. Nucl. Phys. 44, 529 (1987).MathSciNetADSGoogle Scholar
  11. 11.
    C. Vafa, Symposium on Fields, Strings, and Quantum Gravity, Beijing, 1989.Google Scholar
  12. 12.
    C. Vafa and N. P. Warner, Phys. Lett. 218B, 51 (1989).MathSciNetADSGoogle Scholar
  13. 13.
    C. Vafa, Mod. Phys. Lett. A4, 1169, 1615 (1989).MathSciNetADSGoogle Scholar
  14. 14.
    W. Lerche, C. Vafa, N. P. Warner, Nucl. Phys. B324, 427 (1989).MathSciNetADSCrossRefGoogle Scholar
  15. 15.
    E. Martinec, “Criticality, Catastrophe, and Compactifications,” in Physics and Mathematics of Strings, World Scientific, Singapore (1990).Google Scholar
  16. 16.
    V. I. Arnold, Singularity Theory, London Math. Lec. Notes Series, vol. 53, Cambridge University Press, London (1981); V. I. Arnold, S. M. Gusein-Zade, and A. N. Varchenko, Singularities of Differentiable Maps, vol. 1, Birkhauser, Basel (1985).Google Scholar
  17. 17.
    E. Wirten, Comm. Math. Phys. 121, 351 (1989).MathSciNetADSCrossRefGoogle Scholar
  18. 18.
    A. Schwimmer and N. Seiberg, Phys. Lett. 184B, 191 (1987).MathSciNetADSGoogle Scholar
  19. 19.
    O. Alvarez, Nucl. Phys. B216, 125 (1983).ADSCrossRefGoogle Scholar
  20. 20.
    B.R. Greene, C. Vafa, and N.P. Warner, Nucl. Phys. B324, 317 (1989).MathSciNetGoogle Scholar
  21. 21.
    P. Ginsparg, Nucl. Phys. B295, 153 (1988).MathSciNetADSCrossRefGoogle Scholar
  22. 22.
    E. B. Kiritsis, Phys. Lett. 217B, 427 (1988).MathSciNetADSGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Michio Kaku
    • 1
  1. 1.Department of PhysicsCity College of the City University of New YorkNew YorkUSA

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