Differential equations associated to the SU (2) WZNW model on elliptic curves

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Abstract

We study the SU (2) WZNW model over a family of elliptic curves. Starting from the formulation developed in [13], we derive a system of differential equations which contains the Knizhnik-Zamolodchikov-Bernard equations [1][9]. Our system completely determines the N-point functions and is regarded as a natural elliptic analogue of the system obtained in [12] for the projective line. We also calculate the system for the 1-point functions explicitly. This gives a generalization of the results in [7] for sl(2, ℂ)-characters.

Original languageEnglish
Pages (from-to)207-233
Number of pages27
JournalPublications of the Research Institute for Mathematical Sciences
Volume32
Issue number2
Publication statusPublished - Mar 1996
Externally publishedYes

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Elliptic Curves
Differential equation
System of Differential Equations
Model
Analogue
Calculate
Formulation
Line
Character
Generalization
Family

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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abstract = "We study the SU (2) WZNW model over a family of elliptic curves. Starting from the formulation developed in [13], we derive a system of differential equations which contains the Knizhnik-Zamolodchikov-Bernard equations [1][9]. Our system completely determines the N-point functions and is regarded as a natural elliptic analogue of the system obtained in [12] for the projective line. We also calculate the system for the 1-point functions explicitly. This gives a generalization of the results in [7] for sl(2, ℂ)-characters.",
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