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.

arXiv comment36 pages plus tables; v2: minor changes, references added, ancillary files with mathematica notebooks added

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• The low-energy limit of AdS${}_3$/CFT${}_2$ and its TBA
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• 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
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• A review of the AdS/CFT Quantum Spectral Curve
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• 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
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• N=4 SYM Quantum Spectral Curve in BFKL regime
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