# BFKL spectrum of N$$\mathcal{N}$$ = 4: non-zero conformal spin

@article{Alfimov2018BFKLSO,
title={BFKL spectrum of N\$\$ \mathcal\{N\} \$\$ = 4: non-zero conformal spin},
author={M. Alfimov and N. Gromov and G. Sizov},
journal={Journal of High Energy Physics},
year={2018},
volume={2018},
pages={1-78}
}
• Published 2018
• Physics, Mathematics
• Journal of High Energy Physics
A bstractWe developed a general non-perturbative framework for the BFKL spectrum of planar N$$\mathcal{N}$$ = 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… Expand
13 Citations

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#### References

SHOWING 1-10 OF 89 REFERENCES
Quantum spectral curve at work: from small spin to strong coupling in N$$\mathcal{N}$$ = 4 SYM
• Physics, Mathematics
• 2014
A bstractWe apply the recently proposed quantum spectral curve technique to the study of twist operators in planar N$$\mathcal{N}$$ = 4 SYM theory. We focus on the small spin expansion of anomalousExpand
Quantum Spectral Curve and the Numerical Solution of the Spectral Problem in AdS5/CF T4
• Physics
• 2016
A bstractWe developed an efficient numerical algorithm for computing the spectrum of anomalous dimensions of the planar N$$\mathcal{N}$$ = 4 Super-Yang-Mills at finite coupling. The method is basedExpand
Quantum Spectral Curve for a cusped Wilson line in N=4$$\mathcal{N}=4$$ SYM
• Physics
• 2016
A bstractWe show that the Quantum Spectral Curve (QSC) formalism, initially formulated for the spectrum of anomalous dimensions of all local single trace operators in N=4$$\mathcal{N}=4$$ SYM, canExpand
Quantum spectral curve and structure constants in N=4$$\mathcal{N}=4$$ SYM: cusps in the ladder limit
• Physics, Mathematics
• 2018
A bstractWe find a massive simplification in the non-perturbative expression for the structure constant of Wilson lines with 3 cusps when expressed in terms of the key Quantum Spectral CurveExpand
Integrability of conformal fishnet theory
• Physics, Mathematics
• 2017
A bstractWe study integrability of fishnet-type Feynman graphs arising in planar four-dimensional bi-scalar chiral theory recently proposed in arXiv:1512.06704 as a special double scaling limit ofExpand
QCD pomeron from AdS/CFT Quantum Spectral Curve
• Physics
• 2014
A bstractUsing the methods of the recently proposed Quantum Spectral Curve (QSC) originating from integrability of N=4$$\mathcal{N}=4$$ Super-Yang-Mills theory we analytically continue the scalingExpand
Quantum Spectral Curve of γ-Twisted = 4 SYM Theory and Fishnet CFT
We review the quantum spectral curve (QSC) formalism for anomalous dimensions of planar ${\cal\ N}=4$ SYM, including its $\gamma$-deformation. Leaving aside its derivation, we concentrate onExpand
Quantum spectral curve for arbitrary state/operator in AdS5/CFT4
• Physics, Mathematics
• 2015
A bstractWe give a derivation of quantum spectral curve (QSC) — a finite set of Riemann-Hilbert equations for exact spectrum of planar N=4$$\mathcal{N}=4$$ SYM theory proposed in our recent paperExpand
ABJM quantum spectral curve and Mellin transform
• Physics
• 2017
A bstractThe present techniques for the perturbative solution of quantum spectral curve problems in N=4$$\mathcal{N}=4$$ SYM and ABJM models are limited to the situation when the states quantumExpand
Quark-anti-quark potential in N$$\mathcal{N}$$ = 4 SYM
• Physics
• 2016
A bstractWe construct a closed system of equations describing the quark-anti-quark potential at any coupling in planar N$$\mathcal{N}$$ = 4 supersymmetric Yang-Mills theory. It is based on theExpand