NNLO BFKL Pomeron eigenvalue in N=4 SYM

TL;DR

This work delivers an analytic NNLO correction to the BFKL Pomeron eigenvalue in planar $N=4$ SYM through a Quantum Spectral Curve (QSC) perturbative framework. By performing a double expansion around special dimensions $oldsymbol{ ext Delta_0}igr= ext{1,3,5,7}$ and small coupling, the authors obtain $S( ext{Delta})$ and extract the NNLO piece $oldsymbol{F_3(x)}$, which can be written as a uniform-transcendentality sum of nested harmonic sums with 37 nonzero coefficients. The NNLO result is cross-validated against high-precision numerical data (up to ~80 digits, test accuracy ~10^{-61}), and a general analytic perturbative QSC procedure is developed, potentially aiding future QSC-based computations and shedding light on the QCD counterpart via maximal transcendentality. A Mathematica notebook and supporting harmonic-sum tools accompany the results for practical use and verification.

Abstract

We obtain an analytical expression for the Next-to-Next-to-Leading order of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) Pomeron eigenvalue in planar SYM N=4 using Quantum Spectral Curve (QSC) integrability based method. The result is verified with more than 60 digits precision using the numerical method developed by us in a previous paper. As a byproduct we developed a general analytic method of solving the QSC perturbatively.