Communications in Mathematical Physics

, Volume 176, Issue 1, pp 133–161 | Cite as

Conformal blocks on elliptic curves and the Knizhnik-Zamolodchikov-Bernard equations

  • Giovanni Felder
  • Christian Wieczerkowski
Article

Abstract

We give an explicit description of the vector bundle of WZW conformal blocks on elliptic curves with marked points as a subbundle of a vector bundle of Weyl group invariant vector valued theta functions on a Cartan subalgebra. We give a partly conjectural characterization of this subbundle in terms of certain vanishing conditions on affine hyperplanes. In some cases, explicit calculations are possible and confirm the conjecture. The Friedan-Shenker flat connection is calculated, and it is shown that horizontal sections are solutions of Bernard's generalization of the Knizhnik-Zamolodchikov equation.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Vector Bundle 

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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Giovanni Felder
    • 1
  • Christian Wieczerkowski
    • 2
  1. 1.Department of MathematicsUniversity of North Carolina at Chapel HillChapel HillUSA
  2. 2.Institut Für Theoretische Physik IUniversität MünsterMünsterGermany

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