Advertisement

Modular integrals in minimal super Liouville gravity

  • V. A. Belavin
Article

Abstract

We evaluate the four-point integral of the minimal super Liouville gravity on the sphere numerically. The integration procedure is based on the effective elliptic parameterization of the moduli space. We perform the analysis for a few different gravitational four-point amplitudes. The results agree with the analytic results recently obtained using the higher super Liouville equations of motion.

Keywords

super conformal field theory superstring two-dimensional super Liouville gravity 

References

  1. 1.
    A. M. Polyakov, Phys. Lett. B, 103, 211–213 (1981).CrossRefMathSciNetADSGoogle Scholar
  2. 2.
    Al. Zamolodchikov, Internat. J. Mod. Phys. A, 19,Suppl. 2, 510–523 (2004); arXiv:hep-th/0312279v1 (2003).zbMATHCrossRefMathSciNetADSGoogle Scholar
  3. 3.
    A. A. Belavin and Al. B. Zamolodchikov, Theor. Math. Phys., 147, 729–754 (2006); arXiv:hep-th/0510214v1 (2005).CrossRefMathSciNetGoogle Scholar
  4. 4.
    A. Belavin and A. B. Zamolodchikov, JETP Lett., 82, 7–13 (2005).CrossRefADSGoogle Scholar
  5. 5.
    P. Ginsparg and G. Moore, “Lectures on 2D gravity and 2D string theory (TASI 1992),” arXiv:hep-th/9304011v1 (1993); P. Di Francesco, P. Ginsparg, and J. Zinn-Justin, Phys. Rep., 254, 1–133 (1995); arXiv:hep-th/9306153v2 (1993).Google Scholar
  6. 6.
    A. Belavin and A. Zamolodchikov, J. Phys. A, 42, 304004 (2009); arXiv:0811.0450v1 [hep-th] (2008).CrossRefGoogle Scholar
  7. 7.
    A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov, Nucl. Phys. B, 241, 333–380 (1984).zbMATHCrossRefMathSciNetADSGoogle Scholar
  8. 8.
    V. G. Kac, Infinite-Dimensional Lie Algebras (Progr. Math., Vol. 44), Birkhäuser, Boston, Mass. (1983).zbMATHGoogle Scholar
  9. 9.
    A. A. Belavin and Al. B. Zamolodchikov, JETP Lett., 84, 418–424 (2006).CrossRefADSGoogle Scholar
  10. 10.
    A. Belavin and V. Belavin, J. Phys. A, 42, 204003 (2009); arXiv:0810.1023v2 [hep-th] (2008).Google Scholar
  11. 11.
    F. David, Modern Phys. Lett. A, 3, 1651–1656 (1988).CrossRefMathSciNetADSGoogle Scholar
  12. 12.
    J. Distler and H. Kawai, Nucl. Phys. B, 231, 509–527 (1989).CrossRefMathSciNetADSGoogle Scholar
  13. 13.
    J. Distler, Z. Hlousek, and H. Kawai, Internat. J. Mod. Phys. A, 5, 391–414 (1990).CrossRefMathSciNetADSGoogle Scholar
  14. 14.
    A. Belavin, V. Belavin, A. Neveu, and Al. Zamolodchikov, Nucl. Phys. B, 784, 202–233 (2007); arXiv:hep-th/0703084v1 (2007).zbMATHCrossRefMathSciNetADSGoogle Scholar
  15. 15.
    R. H. Poghossian, Nucl. Phys. B, 496, 451–464 (1997).zbMATHCrossRefMathSciNetADSGoogle Scholar
  16. 16.
    R. Rashkov and M. Stanishkov, Phys. Lett. B, 380, 49–58 (1996).CrossRefMathSciNetADSGoogle Scholar
  17. 17.
    T. Fukuda and K. Hosomichi, Nucl. Phys. B, 635, 215–254 (2002); arXiv:hep-th/0202032v3 (2002).zbMATHCrossRefMathSciNetADSGoogle Scholar
  18. 18.
    H. Dorn and H.-J. Otto, Phys. Lett. B, 291, 39–43 (1992); arXiv:hep-th/9206053v1 (1992); Nucl. Phys. B, 429, 375–388 (1994); arXiv:hep-th/9403141v3 (1994).CrossRefMathSciNetADSGoogle Scholar
  19. 19.
    A. Zamolodchikov and Al. Zamolodchikov, Nucl. Phys. B, 477, 577–605 (1996).zbMATHCrossRefMathSciNetADSGoogle Scholar
  20. 20.
    J. Polchinski, String Theory, Vol. 2, Superstring Theory and Beyond, Cambridge Univ. Press, Cambridge (1998).Google Scholar
  21. 21.
    E. Verlinde and H. Verlinde, “Lectures on string perturbation theory,” in: Superstrings’ 88 (M. Green, M. Grisaru, R. Iengo, E. Sezgin, and A. Strominger, eds.), World Scientific, Teaneck, N. J. (1989), pp. 189–250.Google Scholar
  22. 22.
    D. Friedan, JHEP, 0310, 063 (2003); arXiv:hep-th/0204131v1 (2002).CrossRefMathSciNetADSGoogle Scholar
  23. 23.
    Al. B. Zamolodchikov, Theor. Math. Phys., 151, 439–458 (2007); arXiv:hep-th/0604158v1 (2006).zbMATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    L. Hadasz, Z. Jaskolski, and P. Suchanek, Nucl. Phys. B, 798, 363–378 (2008); arXiv:0711.1619v1 [hep-th] (2007).zbMATHCrossRefMathSciNetADSGoogle Scholar
  25. 25.
    L. Hadasz, Z. Jaskólski, and P. Suchanek, JHEP, 0703, 032 (2007); arXiv:hep-th/0611266v1 (2006).CrossRefADSGoogle Scholar
  26. 26.
    V. A. Belavin, Theor. Math. Phys., 152, 1275–1285 (2007); arXiv:hep-th/0611295v2 (2006).zbMATHCrossRefMathSciNetGoogle Scholar
  27. 27.
    V. A. Belavin, Nucl. Phys. B, 798, 423–442 (2008); arXiv:0705.1983v1 [hep-th] (2007).zbMATHCrossRefMathSciNetADSGoogle Scholar
  28. 28.
    D. Chorażkiewicz and L. Hadasz, JHEP, 0901, 007 (2009); arXiv:0811.1226v1 [hep-th] (2008).CrossRefADSGoogle Scholar

Copyright information

© MAIK/Nauka 2009

Authors and Affiliations

  1. 1.Institute for Theoretical and Experimental PhysicsMoscowRussia
  2. 2.Laboratoire de Physique Théorique et AstroparticulesUniversité Montpellier IIMontpellierFrance

Personalised recommendations