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

TL;DR

This paper introduces the Asymptotic Baxter--Bethe Ansatz, a new formalism for analyzing the asymptotic spectrum of Regge trajectories in N=4 SYM, enabling multi-loop calculations and trajectory classification.

Contribution

It develops a novel set of equations that determine the asymptotic spectrum, facilitating systematic perturbative and non-perturbative studies in N=4 SYM.

Findings

Derived multi-loop results in the BFKL regime

Classified Regge trajectories systematically

Provided a framework for strong-coupling analysis

Abstract

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 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 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.