  This work is devoted to the six-gluon scattering amplitude in strongly
coupled N=4 supersymmetric Yang-Mills theory. At weak coupling, an appropriate
high energy limit of the so-called remainder function, i.e. of the deviation
from the BDS formula, may be understood in terms of the lowest eigenvalue of
the BFKL hamiltonian. According to Alday et al., amplitudes in the strongly
coupled theory can be constructed through an auxiliary 1-dimensional quantum
system. We argue that certain excitations of this quantum system determine the
Regge limit of the remainder function at strong coupling and we compute its
precise value.
