N=4 SYM Quantum Spectral Curve in BFKL regime

Abstract

We review the applications of the Quantum Spectral Curve (QSC) method to the Regge (BFKL) limit in N=4 supersymmetric Yang-Mills theory. QSC, based on quantum integrability of the AdS${}_5$/CFT${}_4$ duality, was initially developed as a tool for the study of the spectrum of anomalous dimensions of local operators in the N=4 SYM in the planar, $N_c\to \infty$ limit. We explain how to apply the QSC for the BFKL limit, which requires non-trivial analytic continuation in spin $S$ and extends the initial construction to non-local light-ray operators. We give a brief review of high precision non-perturbative numerical solutions and analytic perturbative data resulting from this approach. We also describe as a simple example of the QSC construction the leading order in the BFKL limit. We show that the QSC substantially simplifies in this limit and reduces to the Faddeev-Korchemsky Baxter equation for Q-functions. Finally, we review recent results for the Fishnet CFT, which carries a number of similarities with the Lipatov's integrable spin chain for interacting reggeized gluons.

arXiv commentContribution to the memorial volume "From the past to the future - the legacy of Lev Lipatov", 28 pages, 7 figures; v2: references added, typos fixed

References in corpus (37)

• The Bethe-Ansatz for N=4 Super Yang-Mills
• Hidden Symmetries of the AdS_5 x S^5 Superstring
• Transcendentality and Crossing
• The Dilatation Operator of Conformal N=4 Super Yang-Mills Theory
• The Pomeron and Gauge/String Duality
• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
• Integrability for the Full Spectrum of Planar AdS/CFT II
• Integrability for the Full Spectrum of Planar AdS/CFT
• Conformal Regge theory
• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• NLO corrections to the BFKL equation in QCD and in supersymmetric gauge theories
• Wrapping interactions and a new source of corrections to the spin-chain/string duality
• The Algebraic Curve of Classical Superstrings on AdS_5xS^5
• Beauty and the Twist: The Bethe Ansatz for Twisted N=4 SYM
• Anomalous dimensions of Wilson operators in N=4 SYM theory
• New integrable non-gauge 4D QFTs from strongly deformed planar N=4 SYM
• The Bulk Dual of SYK: Cubic Couplings
• Gluing Ladders into Fishnets
• Quantum Spectral Curve and the Numerical Solution of the Spectral Problem in AdS5/CFT4
• T-system on T-hook: Grassmannian Solution and Twisted Quantum Spectral Curve
• Strongly γ-deformed N=4 SYM as an integrable CFT
• NNLO BFKL Pomeron eigenvalue in N=4 SYM
• Exact Slope and Interpolating Functions in ABJM Theory
• Quantum spectral curve as a tool for a perturbative quantum field theory
• Bi-scalar integrable CFT at any dimension
• DGLAP and BFKL evolution equations in the N=4 supersymmetric gauge theory
• Quantum Spectral Curve for a Cusped Wilson Line in N=4 SYM
• Interaction of Reggeized Gluons in the Baxter-Sklyanin Representation
• Basso-Dixon Correlators in Two-Dimensional Fishnet CFT
• On a CFT limit of planar ${\gamma }_i$-deformed $\mathcal{N}=4$ SYM theory
• The Holographic Fishchain
• Pomeron in the N=4 supersymmetric gauge model at strong couplings
• A piece of cake: the ground-state energies in gamma_i-deformed N=4 SYM theory
• The role of leading twist operators in the Regge and Lorentzian OPE limits
• Twist-two operators and the BFKL regime - nonstandard solutions of the Baxter equation
• Twistor fishnets
• Conformal Pomeron and Odderon in Strong Coupling

Cited by in corpus (3)

• Solving the Hagedorn temperature of AdS5/CFT4 via the Quantum Spectral Curve: Chemical potentials and deformations
• Universal transcendentality limit of BFKL eigenvalue
• Anomalous dimensions of twist 2 operators and $\mathcal{N}=4$ SYM quantum spectral curve