New formulae for solutions of quantum Knizhnik-Zamolodchikov equations on level -4

Apr, 2003

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Abstract:
We present a new form of solution to the quantum Knizhnik-Zamolodchikov equation on level -4 in a special case corresponding to the Heisenberg XXX spin chain. Our form is equivalent to the integral representation obtained by Jimbo and Miwa in 1996 . An advantage of our form is that it is reduced to the product of single integrals. This fact is deeply related to a cohomological nature of our formulae. Our approach is also based on the deformation of hyper-elliptic integrals and their main property -- deformed Riemann bilinear relation. Jimbo and Miwa also suggested a nice conjecture which relates solution of the qKZ on level -4 to any correlation function of the XXX model. This conjecture together with our form of solution to the qKZ makes it possible to prove a conjecture that any correlation function of the XXX model can be expressed in terms of the Riemann zeta-function at odd arguments and rational coefficients suggested in our previous papers. This issue will be discussed in our next publication.
Note:
  • 15 pages Subj-class: High Energy Physics - Theory: Mathematical Physics: Quantum Algebra Journal-ref: J.Phys. A37 (2004) 323-336