JETP Letters

, Volume 93, Issue 2, pp 47–51 | Cite as

A remark on the three approaches to 2D quantum gravity

Fields, Particles, and Nuclei

Abstract

The one-matrix model is considered. The generating function of the correlation numbers is defined in such a way that this function coincides with the generating function of the Liouville gravity. Using the Kontsevich theorem we explain that this generating function is an analytic continuation of the generating function of the Topological gravity. We check the topological recursion relations for the correlation functions in the p-critical Matrix model.

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References

  1. 1.
    P. H. Ginsparg and G. W. Moore, hep-th/9304011.Google Scholar
  2. 2.
    P. Di Francesco, P. H. Ginsparg, and J. Zinn-Justin, Phys. Rep. 254, 1 (1995); hep-th/9306153.CrossRefADSGoogle Scholar
  3. 3.
    A. A. Belavin and A. B. Zamolodchikov, J. Phys. A 42, 304004 (2009); arxiv:0811.0450.CrossRefMathSciNetGoogle Scholar
  4. 4.
    A. Belavin and G. Tarnopolsky, arxiv:1006.2056v1.Google Scholar
  5. 5.
    V. Belavin, arxiv:10105508v1.Google Scholar
  6. 6.
    A. Belavin and Al. Zamolodchikov, Theor. Math. Phys. 147, 729 (2006); hep-th/0510214.CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    D. J. Gross and A. Migdal, Nucl. Phys. B 340, 333 (1990).CrossRefMathSciNetADSGoogle Scholar
  8. 8.
    E. Witten, Surv. Diff. Geom. 1, 243 (1991).MathSciNetGoogle Scholar
  9. 9.
    M. Kontsevich, Comm. Math. Phys. 147, 1 (1992).CrossRefMATHMathSciNetADSGoogle Scholar
  10. 10.
    E. Getzler, math.AG/9801003.Google Scholar
  11. 11.
    A. B. Zamolodchikov (unpublished).Google Scholar
  12. 12.
    B. Eynard and N. Orantin, math-ph/0702045.Google Scholar
  13. 13.
    M. Bergere and B. Eynard, arXiv:0909.0854v1.Google Scholar
  14. 14.
    Al. B. Zamolodchikov, Theor. Math. Phys. 142, 183 (2005); hep-th/0505063v1.MATHMathSciNetGoogle Scholar
  15. 15.
    E. Witten, Nucl. Phys. B 340, 281 (1990).CrossRefMathSciNetADSGoogle Scholar
  16. 16.
    S. K. Lando and A. K. Zvonkin, Graphs on Surfaces and Their Applications (Springer, Berlin, 2004).MATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  1. 1.Landau Institute for Theoretical PhysicsRussian Academy of SciencesChernogolovka, Moscow regionRussia
  2. 2.Independent University of MoscowMoscowRussia

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