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<p>In this work, we derive a novel set of equations — the <i>Asymptotic Baxter-Bethe Ansatz</i> —that determine the asymptotic spectrum of Regge trajectories in the BFKL regime of <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> <mo>=</mo> <mn>4</mn> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N}=4 \)</EquationSource> </InlineEquation> 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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月3日

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  • Simon Ekhammar,
  • Nikolay Gromov,
  • Michelangelo Preti

摘要

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 \( \mathcal{N}=4 \) 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.