Regge trajectories of $$ \mathcal{N}=4 $$ SYM. Part I. General Asymptotic Baxter-Bethe Ansatz

A bstract 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 BFKL regime of $$ \mathcal{N}=4 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> </mml:math> 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 perturbative data, as we demonstrate, but also enables the classification of trajectories, paving the way for systematic non-perturbative studies up to the strong-coupling regime.