A nonperturbative foundation of the Euclidean-Minkowskian duality of Wilson-loop correlation functions

Understand

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.