Regge Trajectories of N=4 SYM Part I:General Asymptotic Baxter-Bethe Ansatz

In this work, we derive a novel set of equations—the Asymptotic Baxter– Bethe Ansatz—that determine the asymptotic spectrum of Regge trajectories in the BFKLregime of N = 4 SYM. In this challenging limit, our method yields multi-loop results in the’t Hooft coupling, with the perturbative accuracy increasing as the quantum numbers grow.Our formalism not only provides a straightforward path to obtain multi-loop perturbativedata, as we demonstrate, but also enables the classification of trajectories, paving the wayfor systematic non-perturbative studies up to the strong-coupling regime.