New formulae for solutions to quantum Knizhnik–Zamolodchikov equations of level $-4$ and correlation functions

This paper is a continuation of our previous papers [4] and [5]. We discuss the new form of solution to the quantum Knizhnik–Zamolodchikov equation (qKZ) of level -4 obtained in [5] for the Heisenberg XXX spin chain in more detail. The main advantage of this form is that it explicitly reduces to one-dimensional integrals. We believe that the basic mathematical reason for this is some special cohomologies of deformed Jacobi varieties. We apply this new form of the solution to correlation functions by using the Jimbo–Miwa conjecture [7]. Formula (45) for correlation functions obtained in this way is in a good agreement with the ansatz for the emptiness formation probability from [4]. Our previous conjecture describing the structure of correlation functions of the XXX model in the homogeneous limit through the Riemann zeta functions at odd arguments is a corollary to (45).