Hermann Boos, Vladimir Korepin and Feodor Smirnov
New formulae for solutions of quantum Knizhnik-Zamolodchikov
equations on level -4 and correlation functions.
(355K, PostScipt)
ABSTRACT. This paper is continuation of our previous papers hep-th/0209246 and
hep-th/0304077.
We discuss in more detail
a new form of solution to the quantum Knizhnik-Zamolodchikov
equation [qKZ] on level -4 obtained in the paper hep-th/0304077
for the Heisenberg XXX spin chain. The main advantage of this
form is it's explicit reducibility to one-dimensional integrals.
We argue that the deep mathematical reason for this is some
special cohomologies of deformed Jacobi varieties.
We apply this new form of solution
to the correlation functions using the Jimbo-Miwa conjecture.
A formula (46) for the correlation functions obtained in this way
is in a good agreement with the ansatz for the emptiness formation
probability from the paper hep-th/0209246.
Our previous conjecture on a structure of correlation functions of
the XXX model in the homogeneous limit through the Riemann zeta functions
at odd arguments is a corollary of this formula.