# The Multi-Regge Limit from the Wilson Loop OPE

## TL;DR

This paper investigates the multi-Regge limit of the Wilson loop OPE in N=4 super Yang-Mills theory, providing a method to analytically continue and compute the remainder function across all Mandelstam regions, confirmed by two-loop examples.

## Contribution

It introduces a novel analytic continuation approach for the Wilson loop OPE to analyze multi-Regge limits in all Mandelstam regions, including explicit two-loop calculations for heptagon functions.

## Key findings

- The multi-Regge limit depends on Mandelstam regions and can be analyzed via Wilson loop OPE.
- Leading order gluon excitations determine the multi-Regge collinear limit.
- Two-loop heptagon remainder functions are fully determined from their symbols using this method.

## Abstract

The finite remainder function for planar, color-ordered, maximally helicity violating scattering processes in N=4 super Yang-Mills theory possesses a non-vanishing multi-Regge limit that depends on the choice of a Mandelstam region. We analyze the combined multi-Regge collinear limit in all Mandelstam regions through an analytic continuation of the Wilson loop OPE. At leading order, the former is determined by the gluon excitation of the Gubser-Klebanov-Polyakov string. We illustrate the general procedure at the example of the heptagon remainder function at two loops. In this case, the continuation of the leading order terms in the Wilson loop OPE suffices to determine the two-loop multi-Regge heptagon functions in all Mandelstam regions from their symbols. The expressions we obtain are fully consistent with recent results by Del Duca et al.