Multi-Regge Limit of the n-Gluon Bubble Ansatz

We investigate n-gluon scattering amplitudes in the multi-Regge region of N=4 supersymmetric Yang-Mills theory at strong coupling. Through a careful analysis of the thermodynamic bubble ansatz (TBA) for surfaces in AdS5 with n-g(lu)on boundary conditions we demonstrate that the multi-Regge limit probes the large volume regime of the TBA. In reaching the multi-Regge regime we encounter wall-crossing in the TBA for all n>6. Our results imply that there exists an auxiliary system of algebraic Bethe ansatz equations which encode valuable information on the analytical structure of amplitudes at strong coupling.