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Theoretical and Mathematical Physics

, Volume 142, Issue 2, pp 183–196 | Cite as

Three-point function in the minimal Liouville gravity

  • Al. B. Zamolodchikov
Article

Abstract

We revisit the problem of the structure constants of the operator product expansions in the minimal models of conformal field theory, rederiving these previously known constants and presenting them in a form particularly useful in Liouville gravity applications. We discuss the analytic relation between our expression and the structure constant in the Liouville field theory and also give the three- and two-point correlation numbers on the sphere in the minimal Liouville gravity in the general form.

Keywords

conformal field theory Liouville gravity minimal models 

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REFERENCES

  1. 1.
    A. Polyakov, Phys. Lett. B, 103, 207 (1981).CrossRefMathSciNetGoogle Scholar
  2. 2.
    J. Distler and H. Kawai, Nucl. Phys. B, 231, 509 (1989); F. David, Modern Phys. Lett. A, 3, 1651 (1988).Google Scholar
  3. 3.
    I. R. Klebanov, “String theory in two dimensions,” hep-th/9108019 (1991); P. Ginsparg and G. Moore, “Lectures on 2D gravity and 2D string theory (TASI 1992),” hep-th/9304011 (1993); P. Di Francesco, P. Ginsparg, and J. Zinn-Justin, Phys. Rep., 254, 1 (1995).Google Scholar
  4. 4.
    V. Knizhnik, A. Polyakov, and A. Zamolodchikov, Modern Phys. Lett. A, 3, 819 (1988).Google Scholar
  5. 5.
    A. Belavin, A. Polyakov, and A. Zamolodchikov, Nucl. Phys. B, 241, 333 (1984).CrossRefMathSciNetzbMATHGoogle Scholar
  6. 6.
    H. Dorn and H.-J. Otto, Phys. Lett. B, 291, 39 (1992); hep-th/9206053 (1992); Nucl. Phys. B, 429, 375 (1994); hep-th/9403141 (1994).Google Scholar
  7. 7.
    A. B. Zamolodchikov and Al. B. Zamolodchikov, Nucl. Phys. B, 477, 577 (1996); hep-th/9506136 (1995).Google Scholar
  8. 8.
    E. W. Barnes, Proc. London Math. Soc., 31, 358 (1899); Philos. T. Roy. Soc. A, 196, 265 (1901).Google Scholar
  9. 9.
    J. Teschner, Phys. Lett. B, 363, 65 (1995); hep-th/9507109 (1995).Google Scholar
  10. 10.
    V. G. Kac, Infinite Dimensional Lie Algebras: An Introduction (Progr. Math., Vol. 44), Birkhäuser, Boston, Mass. (1983).Google Scholar
  11. 11.
    V. Dotsenko and V. Fateev, Nucl. Phys. B, 251, 691 (1985); Phys. Lett. B, 154, 291 (1985).Google Scholar
  12. 12.
    P. Di Francesco and D. Kutasov, Nucl. Phys. B, 342, 589 (1990).Google Scholar
  13. 13.
    M. Goulian and M. Li, Phys. Rev. Lett. B, 264, 292 (1991).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Al. B. Zamolodchikov
    • 1
    • 2
  1. 1.Laboratoire de Physique MathématiqueUniversité Montpellier IIMontpellierFrance
  2. 2.Institute of Theoretical and Experimental PhysicsMoscowRussia

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