Asymptotic Solutions to the Quantized Knizhnik-Zamolodchikov Equation and Bethe Vectors

Details Asymptotic Solutions to the Quantized Knizhnik-Zamolodchikov Equation and Bethe Vectors Asymptotic Solutions to the Quantized Knizhnik-Zamolodchikov Equation and Bethe Vectors

1994-06-09

arxiv.org/abs/hep-th/9406060v4

Physics

High Energy Physics

High Energy Physics - Theory

30 pages. Minor misprints are corrected

Scientific paper

Asymptotic solutions to the quantized Knizhnik-Zamolodchikov equation associated with $\frak{gl}_{N+1}$ are constructed. The leading term of an asymptotic solution is the Bethe vector -- an eigenvector of the transfer-matrix of a quantum spin chain model. We show that the norm of the Bethe vector is equal to the product of the Hessian of a suitable function and an explicitly written rational function. This formula is an analogue of the Gaudin-Korepin formula for the norm of the Bethe vector. It is shown that, generically, the Bethe vectors form a base for the $\frak{gl}_2$ case.

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