Quantum Spectral Curve and the Numerical Solution of the Spectral Problem in AdS5/CFT4

Abstract

We developed an efficient numerical algorithm for computing the spectrum of anomalous dimensions of the planar $\mathcal{N}=4$ Super-Yang--Mills at finite coupling. The method is based on the Quantum Spectral Curve formalism. In contrast to Thermodynamic Bethe Ansatz, worked out only for some very special operators, this method is applicable for generic states/operators and is much faster and precise due to its Q-quadratic convergence rate. To demonstrate the method we evaluate the dimensions $\Delta$ of twist operators in $sl(2)$ sector directly for any value of the spin $S$ including non-integer values. In particular, we compute the BFKL pomeron intercept in a wide range of the 't Hooft coupling constant with up to $20$ significant figures precision, confirming two previously known from the perturbation theory orders and giving prediction for several new coefficients. Furthermore, we explore numerically a rich branch cut structure for complexified spin $S$.

24 pages, 7 figures; v2: updated data, added strong coupling fits, improvements of the algorithm described in section 3.4; v3: added Mathematica notebook with implementation of the algorithm, minor corrections in the text

References in corpus (5)

• The Pomeron and Gauge/String Duality
• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• The Quantum Spectral Curve of the ABJM theory
• NNLO BFKL Pomeron eigenvalue in N=4 SYM
• Quantum Spectral Curve for a Cusped Wilson Line in N=4 SYM

Cited by in corpus (50)

• Light-ray operators in conformal field theory
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• T-system on T-hook: Grassmannian Solution and Twisted Quantum Spectral Curve
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• Integrability of Conformal Fishnet Theory
• Quantum Spectral Curve and Structure Constants in N=4 SYM: Cusps in the Ladder Limit
• Structure constants at wrapping order
• A symmetry algebra in double-scaled SYK
• Integrability and Conformal Bootstrap: One Dimensional Defect CFT
• The QCD Renormalization Group Equation and the Elimination of Fixed-Order Scheme-and-Scale Ambiguities Using the Principle of Maximum Conformality
• Quantum Spectral Curve for a Cusped Wilson Line in N=4 SYM
• Quark--anti-quark potential in N=4 SYM
• Structure Constants in $\mathcal{N}=4$ SYM at Finite Coupling as Worldsheet $g$-Function
• The full Quantum Spectral Curve for $Ad{S}_4/CF{T}_3$
• Detectors in weakly-coupled field theories
• Excited States of One-Dimensional Defect CFTs from the Quantum Spectral Curve
• Twist-2 at seven loops in planar N=4 SYM theory: Full result and analytic properties
• Separation of Variables in AdS/CFT: Functional Approach for the Fishnet CFT
• The low-energy limit of AdS${}_3$/CFT${}_2$ and its TBA
• The full spectrum of AdS5/CFT4 I: Representation theory and one-loop Q-system
• All five-loop planar four-point functions of half-BPS operators in $\mathcal{N}=4$ SYM
• Extending the Predictive Power of Perturbative QCD
• Bootstrapping $\mathcal{N}=4$ sYM correlators using integrability
• BFKL Spectrum of N=4 SYM: non-Zero Conformal Spin
• The Hagedorn temperature of AdS5/CFT4 via integrability
• The Hagedorn temperature of AdS5/CFT4 at finite coupling via the Quantum Spectral Curve
• Strong coupling results from the numerical solution of the quantum spectral curve
• Exploring the spectrum of planar $Ad{S}_4/CF{T}_3$ at finite coupling
• Colour-Twist Operators I: Spectrum and Wave Functions
• A review of the AdS/CFT Quantum Spectral Curve
• Quantum Spectral Curve of $\gamma$-twisted $\mathcal{N}=4$ SYM theory and fishnet CFT
• The Holographic Dual of Strongly γ-deformed N=4 SYM Theory: Derivation, Generalization, Integrability and Discrete Reparametrization Symmetry
• Solving the Hagedorn temperature of AdS5/CFT4 via the Quantum Spectral Curve: Chemical potentials and deformations
• Open Fishchain in N=4 Supersymmetric Yang-Mills Theory
• Regge trajectories for the (2,0) theories
• Regge spectroscopy of higher twist states in $\mathcal{N}=4$ supersymmetric Yang-Mills theory
• Protected states in $\mbox{AdS}_3$ backgrounds from integrability
• The thermal bootstrap for the critical O(N) model
• Extended systems of Baxter Q-functions and fused flags I: simply-laced case
• N=4 SYM Quantum Spectral Curve in BFKL regime
• The fate of the Konishi multiplet in the β-deformed Quantum Spectral Curve
• Worldsheet dilatation operator for the $AdS$ superstring
• Master symmetry in the $Ad{S}_5\times S^5$ pure spinor string
• Cutting the cylinder into squares: The square form factor
• ABJM quantum spectral curve at twist 1: algorithmic perturbative solution
• On analytical perturbative solution of ABJM quantum spectral curve
• DGLAP and BFKL equations in $\mathcal{N}=4$ SYM: from weak to strong coupling
• Determinant Form of Correlators in High Rank Integrable Spin Chains via Separation of Variables
• Quantum Spectral Curve for AdS${}_3$/CFT${}_2$: a proposal
• Anomalous dimensions of twist 2 operators and $\mathcal{N}=4$ SYM quantum spectral curve