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=4N=4 SYM for any operator in the slsl(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.