Theoretical and Mathematical Physics

, Volume 152, Issue 3, pp 1275–1285 | Cite as

N=1 supersymmetric conformal block recursion relations



We present explicit recursion relations for the four-point superconformal block functions that are essentially particular contributions of the given conformal class to the four-point correlation function. The approach is based on the analytic properties of the superconformal blocks as functions of the conformal dimensions and the central charge of the superconformal algebra. We compare the results with the explicit analytic expressions obtained for special parameter values corresponding to the truncated operator product expansion. These recursion relations are an efficient tool for numerically studying the four-point correlation function in superconformal field theory in the framework of the bootstrap approach, similar to that in the case of the purely conformal symmetry.


N=1 superconformal field theory four-point conformal block function recursion relation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. Zamolodchikov and Al. Zamolodchikov, Nucl. Phys. B, 477, 577–605 (1996); arXiv: hep-th/9506136v2 (1995).MATHCrossRefMathSciNetADSGoogle Scholar
  2. 2.
    H. Dorn and H.-J. Otto, Nucl. Phys. B, 429, 375–388 (1994); arXiv:hep-th/9403141v3 (1994).MATHCrossRefMathSciNetADSGoogle Scholar
  3. 3.
    J. Teschner, Class. Q. Grav., 18, R153–R222 (2001); arXiv:hep-th/0104158v3 (2001).MATHCrossRefMathSciNetADSGoogle Scholar
  4. 4.
    Al. Zamolodchikov, Internat. J. Mod. Phys. A, 19, No. Suppl. 2, 510–523 (2004); arXiv: hep-th/0312279v1 (2003).MATHCrossRefMathSciNetADSGoogle Scholar
  5. 5.
    Al. B. Zamolodchikov, Theor. Math. Phys., 142, 183–196 (2005); arXiv:hep-th/0505063v1 (2005).MathSciNetGoogle Scholar
  6. 6.
    A. A. Belavin and Al. B. Zamolodchikov, Theor. Math. Phys., 147, 729–754 (2006).CrossRefMathSciNetGoogle Scholar
  7. 7.
    A. M. Polyakov, Phys. Lett. B, 103, 211–213 (1981).CrossRefMathSciNetADSGoogle Scholar
  8. 8.
    A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov, Nucl. Phys. B, 241, 333–380 (1984).MATHCrossRefMathSciNetADSGoogle Scholar
  9. 9.
    Al. Zamolodchikov, Comm. Math. Phys., 96, 419–422 (1984).CrossRefMathSciNetADSGoogle Scholar
  10. 10.
    A. B. Zamolodchikov and R. G. Pogosyan, Sov. J. Nucl. Phys., 47, 929–936 (1988).MathSciNetGoogle Scholar
  11. 11.
    L. Alvarez-Gaumé and P. Zaugg, Ann. Phys., 215, 171–230 (1992); arXiv: hep-th/9109050v1 (1991).MATHCrossRefADSGoogle Scholar
  12. 12.
    V. G. Kac, Infinite-Dimensional Lie Algebras: An Introduction (Progr. Math., Vol. 44), Birkhä user, Boston (1983).MATHGoogle Scholar
  13. 13.
    A. A. Belavin and Al. B. Zamolodchikov, JETP Lett., 84, 418–424 (2006); arXiv: hep-th/0610316v2 (2006).CrossRefADSGoogle Scholar
  14. 14.
    A. B. Zamolodchikov and Al. B. Zamolodchikov, “Conformal field theory and 2-D critical phenomena: Part III. Conformal bootstrap and degenerate representations of conformal algebra,” Preprint ITEP-90-31, Inst. Theor. Exper. Phys., Moscow (1990).Google Scholar
  15. 15.
    Al. B. Zamolodchikov, Theor. Math. Phys., 73, 1088–1093 (1987).CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.Institute for Theoretical and Experimental PhysicsMoscowRussia
  2. 2.International School for Advanced Studies (SISSA)TriesteItaly

Personalised recommendations