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

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Abstract

We work out finite-dimensional integral formulae for the scalar product of genus one states of the groupG Chern-Simons theory with insertions of Wilson lines. Assuming convergence of the integrals, we show that unitarity of the elliptic Knizhnik-Zamolodchikov-Bernard connection with respect to the scalar product of CS states is closely related to the Bethe Ansatz for the commuting Hamiltonians building up the connection and quantizing the quadratic Hamiltonians of the elliptic Hitchin system.

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Authors and Affiliations

  1. Depto. Física Teórica, Univ. Zaragoza, E-50009, Zaragoza, Spain

    Fernando Falceto

  2. I.H.E.S., C.N.R.S., F-91440, Bures-sur-Yvette, France

    Krzysztof Gawędzki

Authors
  1. Fernando Falceto
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  2. Krzysztof Gawędzki
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Communicated by G. Felder

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Falceto, F., Gawędzki, K. Unitarity of the Knizhnik-Zamolodchikov-Bernard connection and the Bethe Ansatz for the elliptic Hitchin systems. Commun.Math. Phys. 183, 267–290 (1997). https://doi.org/10.1007/BF02506407

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  • DOI: https://doi.org/10.1007/BF02506407

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