TY - JOUR

T1 - BFKL spectrum of N = 4: non-zero conformal spin

AU - Gromov, Nikolay

AU - Sizov, Grigory Alekseevich

AU - Alfimov, Mikhail

PY - 2018/7/31

Y1 - 2018/7/31

N2 - 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, 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.

AB - 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, 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.

UR - https://link.springer.com/article/10.1007%2FJHEP07%282018%29181

U2 - 10.1007/JHEP07(2018)181

DO - 10.1007/JHEP07(2018)181

M3 - Article

SN - 1126-6708

VL - 181

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

ER -