Advertisement

Communications in Mathematical Physics

, Volume 163, Issue 1, pp 173–184 | Cite as

On algebraic equations satisfied by hypergeometric correlators in WZW models. I

  • Boris Feigin
  • Vadim Schechtman
  • Alexander Varchenko
Article

Abstract

It is proven that integral expressions for conformal correlators insl(2) WZW model found in [SV] satisfy certain natural algebraic equations. This implies that the above integrals really take their values in spaces of conformal blocks.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Algebraic Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [FSV] Feigin, B., Schechtman, V., Varchenko, A.: On algebraic equations satisfied by correlators in Wess-Zumino-Witten models. Lett. Math. Phys.20, 291–297 (1990)CrossRefGoogle Scholar
  2. [K] Kac, V.: Infinite dimensional Lie algebras. Cambridge: Cambridge Univ. Press, 1985Google Scholar
  3. [KZ] Knizhnik, V., Zamolodchikov, A.: Current algebra and Wess-Zumino model in two dimensions. Nucl. Phys.B247, 83 (1984)CrossRefGoogle Scholar
  4. [SV] Schechtman, V., Varchenko, A.: Arrangements of hyperplanes and Lie algebra homology. Invent. Math.106, 134–194 (1991)CrossRefGoogle Scholar
  5. [TK] Tsuchia, A., Kanie, V.: Vertex operators in conformal field theory on ℙ1 and monodromy representations of braid groups. Adv. Stud. Pure Math.16, 297–372 (1988)Google Scholar
  6. [V] Varchenko, A.: The function\(\prod\limits_{i< j} {(t_i - t_j )^{a_{ij} /\kappa } } \) and the representation theory of Lie algebras and quantum groups. Preprint, 1992Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Boris Feigin
    • 1
  • Vadim Schechtman
    • 2
  • Alexander Varchenko
    • 3
  1. 1.Landau Institute for Theoretical PhysicsMoscowRussia
  2. 2.Dept. of MathematicsSUNY at Stony BrookStony BrookUSA
  3. 3.Dept. of MathematicsUniversity of North Carolina at Chapel HillChapel HillUSA

Personalised recommendations