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.
Keywords
Cite
@article{arxiv.1411.4758,
title = {Quantum spectral curve as a tool for a perturbative quantum field theory},
author = {Christian Marboe and Dmytro Volin},
journal= {arXiv preprint arXiv:1411.4758},
year = {2015}
}
Comments
36 pages plus tables; v2: minor changes, references added, ancillary files with mathematica notebooks added