  In this letter we discuss the analyticity properties of the Wilson-loop
correlation functions relevant to the problem of soft high-energy scattering,
directly at the level of the functional integral, in a genuinely
nonperturbative way. The strategy is to start from the Euclidean theory and to
push the dependence on the relevant variables $\theta$ (the relative angle
between the loops) and $T$ (the half-length of the loops) into the action by
means of a field and coordinate transformation, and then to allow them to take
complex values. In particular, we determine the analyticity domain of the
relevant Euclidean correlation function, and we show that the corresponding
Minkowskian quantity is recovered with the usual double analytic continuation
in $\theta$ and $T$ inside this domain. The formal manipulations of the
functional integral are justified making use of a lattice regularisation. The
new rescaled action so derived could also be used directly to get new insights
(from first principles) in the problem of soft high-energy scattering.
