Abstract
We developed a general non-perturbative framework for the BFKL spectrum of planar mathcal{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, Δ = 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 [1] 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.
Highlights
N = 4 Super-Yang-Mills theory has been playing an important role in our understanding of Quantum Field Theories, especially in an AdS/CFT context
We developed a general non-perturbative framework for the BFKL spectrum of planar N = 4 SYM, based on the Quantum Spectral Curve (QSC)
As the part of the harmonic sum consisting of the nested harmonic sums of the transcendentality 7, which constitutes the rational part at the points n = 4k + 1, was not fitted we are unable to write an expression for the NNNLO intercept working for all conformal spins leaving this task for future studies
Summary
In [20] the 4-loop Asymptotic Bethe Ansatz (ABA) contribution to the anomalous dimension of the twist-2 sl(2) operators was analytically continued to the non-integer spins and compared with the corresponding prediction from the BFKL Pomeron eigenvalues. A very efficient numerical algorithm was constructed in [1], which allows to study the BFKL limit of the spectrum of the theory, but the whole anomalous dimension of a given operator for arbitrary values of the charges. Numerical results for the operator trajectories we were able to fit the numerical values of the BFKL kernel eigenvalues, which were confirmed in [27] using a different method Another method available within the QSC formalism is an efficient perturbative expansion developed in [23, 28,29,30,31].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
