Quantum spectral curve as a tool for a perturbative quantum field theory

Abstract

An iterative procedure perturbatively solving the quantum spectral curve of planar N=4 SYM for any operator in the sl(2) sector is presented. A Mathematica notebook executing this procedure is enclosed. The obtained results include 10-loop computations of the conformal dimensions of more than ten different operators. We prove that the conformal dimensions are always expressed, at any loop order, in terms of multiple zeta-values with coefficients from an algebraic number field determined by the one-loop Baxter equation. We observe that all the perturbative results that were computed explicitly are given in terms of a smaller algebra: single-valued multiple zeta-values times the algebraic numbers.

36 pages plus tables; v2: minor changes, references added, ancillary files with mathematica notebooks added

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Cited by in corpus (57)

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• Fast analytic solver of rational Bethe equations
• Double Wick rotating Green-Schwarz strings
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• Cutting through form factors and cross sections of non-protected operators in N=4 SYM
• Spin Chain Overlaps and the Twisted Yangian
• The full Quantum Spectral Curve for $Ad{S}_4/CF{T}_3$
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• Excited States of One-Dimensional Defect CFTs from the Quantum Spectral Curve
• The low-energy limit of AdS${}_3$/CFT${}_2$ and its TBA
• Separation of Variables in AdS/CFT: Functional Approach for the Fishnet CFT
• Quantum Spectral Curve for the eta-deformed AdS_5xS^5 superstring
• The full spectrum of AdS5/CFT4 I: Representation theory and one-loop Q-system
• 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
• Quantum Spectral Curve of $\gamma$-twisted $\mathcal{N}=4$ SYM theory and fishnet CFT
• A review of the AdS/CFT Quantum Spectral Curve
• Solving the Hagedorn temperature of AdS5/CFT4 via the Quantum Spectral Curve: Chemical potentials and deformations
• Structure constants of short operators in planar $\mathcal{N}=4$ SYM theory
• Six-loop anomalous dimension of twist-two operators in planar N=4 SYM theory
• Non-planar universal anomalous dimension of twist-two operators with general Lorentz spin at four loops in N=4 SYM theory
• BFKL pomeron in the next-to-next-to-leading approximation in the planar N=4 SYM theory
• Integrable strings for AdS/CFT
• ABJM quantum spectral curve and Mellin transform
• Regge spectroscopy of higher twist states in $\mathcal{N}=4$ supersymmetric Yang-Mills theory
• Non-planar cusp and transcendental anomalous dimension at four loops in N=4 supersymmetric Yang-Mills theory
• N=4 SYM Quantum Spectral Curve in BFKL regime
• Worldsheet dilatation operator for the $AdS$ superstring
• Evaluation of the operatorial Q-system for non-compact super spin chains
• The fate of the Konishi multiplet in the β-deformed Quantum Spectral Curve
• S-duality invariant perturbation theory improved by holography
• Bootstrability in Defect CFT: Integrated Correlators and Sharper Bounds
• Cutting the cylinder into squares: The square form factor
• The full spectrum of AdS${}_5$/CFT${}_4$ II: Weak coupling expansion via the quantum spectral curve
• ABJM quantum spectral curve at twist 1: algorithmic perturbative solution
• Master symmetry in the $Ad{S}_5\times S^5$ pure spinor string
• On analytical perturbative solution of ABJM quantum spectral curve
• DGLAP and BFKL equations in $\mathcal{N}=4$ SYM: from weak to strong coupling
• Extensive numerical study of a D-brane, anti-D-brane system in AdS5/CFT4
• Determinant Form of Correlators in High Rank Integrable Spin Chains via Separation of Variables
• NNNLLA BFKL pomeron eigenvalue in the planar N=4 SYM theory
• Quantum Spectral Curve for AdS${}_3$/CFT${}_2$: a proposal
• The Omega-Infinity Limit of Single Spikes
• Orthogonality of Q-Functions up to Wrapping in Planar N=4 Super Yang-Mills Theory
• Anomalous dimensions of twist 2 operators and $\mathcal{N}=4$ SYM quantum spectral curve
• A hitchhiker's guide to quantum field theoretic aspects of $\mathcal{N}=4$ SYM theory and its deformations