On differential equation on four-point correlation function in the conformal Toda field theory

  • V. A. Fateev
  • A. V. Litvinov
Methods of Theoretical Physics

Abstract

The properties of completely degenerate fields in the conformal Toda field theory are studied. It is shown that a generic four-point correlation function that contains only one such field does not satisfy an ordinary differential equation, in contrast to the Liouville field theory. Some additional assumptions for other fields are required. Under these assumptions, we write such a differential equation and solve it explicitly. We use the fusion properties of the operator algebra to derive a special set of three-point correlation functions. The result agrees with the semiclassical calculations.

PACS numbers

11.25.Hf 

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References

  1. 1.
    J. L. Gervais, hep-th/9310116.Google Scholar
  2. 2.
    P. C. West, hep-th/9309095.Google Scholar
  3. 3.
    V. A. Fateev and S. L. Lukyanov, Int. J. Mod. Phys. A 7, 853 (1992).ADSMathSciNetGoogle Scholar
  4. 4.
    A. A. Belavin, Adv. Stud. Pure Math. 19, 117 (1989).MATHMathSciNetGoogle Scholar
  5. 5.
    V. A. Fateev and A. B. Zamolodchikov, Zh. Éksp. Teor. Fiz. 89, 380 (1985) [Sov. Phys. JETP 62, 215 (1985)].MathSciNetGoogle Scholar
  6. 6.
    V. A. Fateev and S. L. Lukyanov, Int. J. Mod. Phys. A 3, 507 (1988).ADSMathSciNetGoogle Scholar
  7. 7.
    V. A. Fateev, hep-th/0103014.Google Scholar
  8. 8.
    A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov, Nucl. Phys. B 241, 333 (1984).CrossRefADSMathSciNetGoogle Scholar
  9. 9.
    V. S. Dotsenko and V. A. Fateev, Nucl. Phys. B 240, 312 (1984).CrossRefADSMathSciNetGoogle Scholar
  10. 10.
    V. S. Dotsenko and V. A. Fateev, Nucl. Phys. B 251, 691 (1985).ADSMathSciNetGoogle Scholar
  11. 11.
    Higher Transcendental Functions (Bateman Manuscript Project), Ed. by A. Erdelyi (McGraw-Hill, New York, 1955; Nauka, Moscow, 1967), Vol. 3.Google Scholar
  12. 12.
    V. Fateev, A. B. Zamolodchikov, and A. B. Zamolodchikov, hep-th/0001012.Google Scholar
  13. 13.
    A. B. Zamolodchikov and A. B. Zamolodchikov, Nucl. Phys. B 477, 577 (1996).CrossRefADSMathSciNetGoogle Scholar
  14. 14.
    C. B. Thorn, Phys. Rev. D 66, 027702 (2002).Google Scholar
  15. 15.
    M. Goulian and M. Li, Phys. Rev. Lett. 66, 2051 (1991).CrossRefADSGoogle Scholar
  16. 16.
    V. A. Fateev (unpublished).Google Scholar
  17. 17.
    G. W. Moore, N. Seiberg, and M. Staudacher, Nucl. Phys. B 362, 665 (1991).CrossRefADSMathSciNetGoogle Scholar
  18. 18.
    N. Seiberg, Prog. Theor. Phys. Suppl. 102, 319 (1990).MATHMathSciNetGoogle Scholar
  19. 19.
    M. A. Olshanetsky and A. M. Perelomov, Phys. Rep. 71, 313 (1981).CrossRefADSMathSciNetGoogle Scholar
  20. 20.
    E. Stade, Duke Math. J. 60, 313 (1990).CrossRefMATHMathSciNetGoogle Scholar
  21. 21.
    S. Kharchev and D. Lebedev, Lett. Math. Phys. 50, 53 (1999).CrossRefMathSciNetGoogle Scholar
  22. 22.
    S. Kharchev and D. Lebedev, Pis’ma Zh. Éksp. Teor. Fiz. 71, 338 (2000) [JETP Lett. 71, 235 (2000)].Google Scholar
  23. 23.
    E. Stade, Isr. J. Math. 127, 201 (2002).MATHMathSciNetGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2005

Authors and Affiliations

  • V. A. Fateev
    • 1
    • 2
  • A. V. Litvinov
    • 1
  1. 1.Landau Institute for Theoretical PhysicsRussian Academy of SciencesChernogolovka, Moscow regionRussia
  2. 2.Laboratoire de Physique Théorique et AstroparticulesUniversité Montpelier IIMontpelierFrance

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