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arXiv · 1411.4758

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

Christian Marboe·Dmytro Volin
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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.

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Christian Marboe, Dmytro Volin. 2015-06-23. Quantum spectral curve as a tool for a perturbative quantum field theory. https://doi.org/10.1016/j.nuclphysb.2015.08.021

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