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

TL;DR

This paper introduces a non-perturbative framework based on the Quantum Spectral Curve for analyzing the BFKL spectrum in N=4 SYM with arbitrary conformal spin, providing new analytic and numerical results.

Contribution

It extends the BFKL spectrum analysis to arbitrary conformal spin using the QSC, reproduces known results, and offers new non-perturbative and high-order perturbative predictions.

Findings

Reproduced all known perturbative BFKL eigenvalues.

Derived new non-perturbative analytic results near |n|=1, Δ=0.

Obtained explicit formulas for the intercept function up to 3-loop order.

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.