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BFKL Spectrum of N=4 SYM: non-Zero Conformal Spin

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arxiv 1802.06908 v4 pith:FTUGC4EX submitted 2018-02-19 hep-th hep-phmath-phmath.MPnucl-th

Mikhail Alfimov , Nikolay Gromov , Grigory Sizov This is my paper · ORCID
classification hep-thhep-phmath-phmath.MPnucl-th
keywords spinbfklconformalarbitraryeigenvaluespectrumanalyticarxiv
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We developed a general non-perturbative framework for the BFKL spectrum of planar N=4 SYM, based on the Quantum Spectral Curve (QSC). It allows one to study the spectrum in the whole generality, extending previously known methods to arbitrary values of conformal spin $n$. We show how to apply our approach to reproduce all known perturbative results for the Balitsky-Fadin-Kuraev-Lipatov (BFKL) Pomeron eigenvalue and get new predictions. In particular, we re-derived the Faddeev-Korchemsky Baxter equation for the Lipatov spin chain with non-zero conformal spin reproducing the corresponding BFKL kernel eigenvalue. We also get new non-perturbative analytic results for the Pomeron eigenvalue in the vicinity of $|n|=1,\;\Delta=0$ point and we obtained an explicit formula for the BFKL intercept function for arbitrary conformal spin up to the 3-loop order in the small coupling expansion and partial result at the 4-loop order. In addition, we implemented the numerical algorithm of arXiv:1504.06640 as an auxiliary file to this arXiv submission. From the numerical result we managed to deduce an analytic formula for the strong coupling expansion of the intercept function for arbitrary conformal spin.

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Cited by 5 Pith papers

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  1. The next-to-next-to-leading order BFKL eigenvalue at odd conformal spin in planar N=4 super Yang-Mills: closed form, coefficient structure, and arithmetic

    hep-th 2026-07 conditional novelty 8.0 of 10

    The NNLO BFKL eigenvalue of planar N=4 SYM is given in closed form at every odd conformal spin via exact Mellin extraction from the Caron-Huot–Herranen integrand, matching quantum spectral curve intercepts through n=91.

  2. The next-to-next-to-leading order BFKL eigenvalue at odd conformal spin in planar N=4 super Yang-Mills

    hep-th 2026-07 conditional novelty 7.0 of 10

    The NNLO BFKL eigenvalue of planar N=4 SYM is now in closed form at every odd spin n, with ν=0 intercepts matching Quantum Spectral Curve data through n=91.

  3. Chaos in the butterfly cone

    hep-th 2019-08 conditional novelty 7.0 of 10

    The velocity-dependent Lyapunov exponent inside the butterfly cone satisfies λ(v) ≤ 2πT(1-|v|/v_B), a generalization of the chaos bound, saturated in SYK chains, holographic theories, and large N CFTs.

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

    hep-th 2025-07 conditional novelty 6.0 of 10

    From the Quantum Spectral Curve, the authors derive the Asymptotic Baxter-Bethe Ansatz, which determines the asymptotic BFKL spectrum of Regge trajectories in N=4 SYM, reproduces known weak-coupling results, and suppo...

  5. DGLAP and BFKL equations in $\mathcal{N}=4$ SYM: from weak to strong coupling

    hep-th 2019-08 unverdicted

    A review of known results on DGLAP and BFKL equations in N=4 SYM, from weak-coupling perturbation theory to strong coupling via AdS/CFT and integrability, with no new derivations.

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