Advertisement

Communications in Mathematical Physics

, Volume 156, Issue 1, pp 179–200 | Cite as

Multivalued fields on the complex plane and conformal field theories

  • Franco Ferrari
Article

Abstract

In this paper a class of conformal field theories with nonabelian and discrete group of symmetry is investigated. These theories are realized in terms of free scalar fields starting from the simpleb-c systems and scalar fields on algebraic curves. The Knizhnik-Zamolodchikov equations for the conformal blocks can be explicitly solved. Besides the fact that one obtains in this way an entire class of theories in which the operators obey nonstandard statistics, these systems are interesting in exploring the connection between statistics and curved space-times, at least in the two dimensional case.

Keywords

Neural Network Statistical Physic Field Theory Complex System Nonlinear Dynamics 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Zamolodchikov, A.B.: Nucl. Phys. B285, [FS19] 481 (1987)CrossRefGoogle Scholar
  2. 2.
    Knizhnik, V.G.: Sov. Phys. Usp.32 (11), 945 (1989)Google Scholar
  3. 3.
    Bershadsky, M.A., Radul, A.O.: Int. J. Mod. Phys. A2, 165 (1987)CrossRefGoogle Scholar
  4. 4.
    Bershadsky, M.A., Radul, A.: Phys. Lett193B, 21 (1987)Google Scholar
  5. 5.
    Dixon, L., Friedan, D., Martinec, E., Shenker, S.: Nucl. Phys. B282, 13 (1987); Hamidi, S., Vafa, C.: Nucl. Phys. B279, 465 (1987); Atick, J.J., Sen, A.: Nucl. Phys. B286, 189 (1987); Vonora, L., Matone, M., Toppan, F., Wu, K.: Phys. Lett.224B, 115 (1989); Nucl. Phys. B334, 717 (1990); Guadagnini, E., Martellini, M., Mintchev, M.: J. Math. Phys.31, 1226 (1990)CrossRefGoogle Scholar
  6. 6.
    Raina, A.K.: Helv. Phys. Acta63, 694 (1990)Google Scholar
  7. 7.
    Ferrari, F.: Phys. Lett.277B 423 (1992)Google Scholar
  8. 8.
    Sato, M., Miwa, T., Jimbo, M.: Holonomic quantum fields (Kyoto U.P. Kyoto), part I; 14 (1978) p. 223; II: 15 (1979) p. 201; III: 15 (1979) p. 577; IV: 15 (1979) p. 871; V; 16 (1980) p. 531Google Scholar
  9. 9.
    Chudnowski, D.V.: In Bifurcation Phenomena in Mathematical Physics and Related Topics. Bardos, C., Bessis, D. (eds.) D. Reidel Publishing Company 1980Google Scholar
  10. 10.
    Blok, B., Yankielowicz, S.: Nucl. Phys. B321, 327 (1989); Blok, B., Yankielowicz: Phys. Lett.226B, 279 (1989)CrossRefGoogle Scholar
  11. 11.
    Ferrari, F.: Int. J. Mod. Phys. A5, 2799 (1990)CrossRefGoogle Scholar
  12. 12.
    Kohno, T.: Nagoya Math. J.92, 21 (1983); Invent. Math.82, 57 (1985)Google Scholar
  13. 13.
    Tsuchiya, A., Kanie, Y.: Lett. Math. Phys.13, 303 (1987)CrossRefGoogle Scholar
  14. 14.
    Blok, B., Wen, X.G.: Nucl. Phys. B374, 615 (1992)CrossRefGoogle Scholar
  15. 15.
    Ferrari, F.: Preprint LMU-TPW 92-24Google Scholar
  16. 16.
    Knizhnik, V.G., Zamolodchikov, A.B.: Nucl. Phys. B247, 83 (1984)CrossRefGoogle Scholar
  17. 17.
    Fröhlich, J.: Statistics of fields, The Yang-Baxter equation and the theory of knots and links. In: Nonperturbative quantum field theory. G. t'Hooft et al. (eds.) New York: Plenum 1988Google Scholar
  18. 18.
    Mack, G., Schomerus, V.: Nucl. Phys. B370, 185 (1992)CrossRefGoogle Scholar
  19. 19.
    Griffiths, H., Harris, J.: New York: Wiley Interscience 1978Google Scholar
  20. 20.
    Fröhlich, J., Marchetti, P.A.: Commun. Math. Phys.112, 343 (1987)CrossRefGoogle Scholar
  21. 21.
    Friedan, D., Martinec, S., Shenker, S.: Nucl. Phys. B271, 93 (1986)CrossRefGoogle Scholar
  22. 22.
    Verlinde, E., Verlinde, H.: Nucl. Phys. B288, 357 (1987)CrossRefGoogle Scholar
  23. 23.
    Bonini, M., Iengo, R.: Int. J. Mod. Phys. A3, 841 (1988)CrossRefGoogle Scholar
  24. 24.
    Ferrari, F.: J. Math. Phys.32 (8), 2186 (1991)CrossRefGoogle Scholar
  25. 25.
    Verlinde, E., Verlinde, H.: Nucl. Phys. B288, 357 (1987)CrossRefGoogle Scholar
  26. 26.
    Bonini, M., Iengo, R.: Int. J. Mod. Phys. A3, 841 (1988)CrossRefGoogle Scholar
  27. 27.
    Mack, G., Schomerus, V.: Nucl. Phys. B370, 185 (1992)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Franco Ferrari
    • 1
  1. 1.Sektion Physik der Universität MünchenMünchenGermany

Personalised recommendations