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

TL;DR

This paper introduces an iterative method to solve the quantum spectral curve in planar N=4 SYM, enabling high-loop computations of operator dimensions and revealing their algebraic structure in terms of multiple zeta-values.

Contribution

It presents a new iterative procedure for solving the quantum spectral curve perturbatively, including a Mathematica implementation and high-loop calculations.

Findings

Computed 10-loop conformal dimensions for over ten operators

Proved dimensions are expressed in terms of multiple zeta-values with algebraic coefficients

Identified a smaller algebra involving single-valued multiple zeta-values

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.