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

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