Unitarity of the Knizhnik-Zamolodchikov-Bernard connection and the Bethe Ansatz for the elliptic Hitchin systems

Communications in Mathematical Physics

Volumn 183, Issue 2, 1997, Pages 267-290

  Falceto, Fernando ^a   Gawędzki, Krzysztof ^b  

^a UNIVERSITY OF ZARAGOZA   (Spain)

^b INSTITUT DES HAUTES ÉTUDES SCIENTIFIQUES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040515491     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02506407     Document Type: Article

References (30)

1. Babujian, H.M.: Off-Shell Bethe Ansatz Equation and N-point Correlators in the SU(2) WZNW Theory. Preprint Bonn-HE-93-22
2. Babujian, H.M., Flume, R.: Off-Shell Bethe Ansatz Equation for Gaudin Magnets and Solutions of Knizhnik-Zamolodchikov Equations. Preprint Bonn-HE-93-30, hep-th/9310110
3. Bernard, D.: On the Wess-Zumino-Witten Models on the Torus. Nucl. Phys. B 303, 77-93 (1988)
4. Donagi, R., Witten, E.: Supersymmetric Yang-Mills Theory and Integrable Systems. hep-th/9510101
5. Enriquez, B., Rubtsov, V.: Hitchin Systems, Higher Gaudin Operators and r-Matrices. alg-geom/9503010
6. Etingof, P., Kirillov, A., Jr.: Representations of Affine Lie Algebras, Parabolic Differential Equations and Lamé Functions. Duke Math. J. 74, 585-614 (1994)
7. Etingof, P., Frenkel, I., Kirillov, A., Jr.: Spherical Functions on Affine Lie Groups. hep-th/9407047
8. Falceto, F., Gawȩdzki, K.: Chern-Simons States at Genus One. Commun. Math. Phys. 159, 549-579 (1994)
9. Falceto, F., Gawȩdzki, K.: Elliptic Wess-Zumino-Witten Model from Elliptic Chern-Simons Theory. Lett. Math. Phys., in press
10. Falceto, F., Gawȩdzki, K., Kupiainen, A.: Scalar Product of Current Blocks in WZW Theory. Phys. Lett. B 260, 101-108 (1991)
11. Feigin, B., Frenkel, E., Reshethikin, N.: Gaudin Model, Bethe Ansatz and Correlation Functions at the Critical Level. hep-th/9402022
12. Felder, G., Varchenko, A.: Integral Representations of Solutions of the Elliptic Knizhnik-Zamolodchikov-Bernard equations. hep-th
13. Felder, G., Varchenko, A.: Three Formulas for Eigenfunctions of Integrable Schroedinger Operators. hep-th/9511120
14. Felder, G., Wieczerkowski, C.: Conformal Blocks on Elliptic Curves and the Knizhnik-Zamolodchikov-Bernard Equations. hep-th/9411004
15. Gaudin, M.: Les fonctions d'onde de Bethe. Paris: Masson, 1983
16. Gawȩdzki, K.: Wess-Zumino-Witten Conformal Field Theories. In: Constructive quantum field theory II, eds. Wightman, A.A., Velo, G., New York: Plenum, 1990, pp. 89-120
17. Gawȩdzki, K.: Quadrature of Conformal Field Theories. Nucl. Phys. B 328, 733-752 (1989)
18. Gawȩdzki, K.: Constructive Conformal Field Theory. In: Functional integration, geometry and strings, eds. Haba, Z., Sobczyk, J. Basel, Boston, Berlin: Birkhäuser, 1989, pp. 277-302
19. Gawȩdzki, K.: SU(2) WZW Theory at higher Genera. Commun. Math. Phys., in press
20. Gawȩdzki, K.: Coulomb Gas Representation of the SU(2) WZW Correlators at Higher Genera. hep-th/9404012, Lett. Math. Phys., in press
21. Gawȩdzki, K., Kupiainen, A.: Coset Construction from Functional Integral. Nucl. Phys. B 320, 625-668 (1989)
22. Hitchin, N.: Stable Bundles and Integrable Systems. Duke Math. J. 54, 91-114 (1987)
23. Knizhnik, V., Zamolodchikov, A.B.: Current Algebra and Wess-Zumino Model in Two Dimensions. Nucl. Phys. B 247, 83-103 (1984)
24. Nekrasov, N.: Holomorphic Bundles and Many-Body Systems. hep-th/9503157
25. Olshanetsky, M.: Generalized Hitchin Systems and Knizhnik-Zamolodchikov-Bernard Equation on Elliptic Curves. hep-th/9510143
26. Reshethikin, N., Varchenko, A.: Quasiclassical Asymptotics of Solutions of the KZ Equation. hep-th/9402126
27. Schechtman, V., Varchenko, A.: Integral Representations of N-point Conformal Correlators in the WZW Model. Preprint MPI/98-51 (1989)
28. Schechtman, V., Varchenko, A.: Arrangements of Hyperplanes and Lie Algebra Homology. Inv. Math. 106, 139-194 (1991)
29. Tsuchiya, A., Kanie, Y.: Vertex Operators in the Conformal Field Theory on P1 and Monodromy Representations of the Braid Group. Adv. Stud. Pure Math. 16, 297-372 (1988)
30. Whittaker, E.T., Watson, G.N.: Course of modern analysis. Cambridge: Cambridge Univ. Press, 1958