pith. machine review for the scientific record. sign in

arxiv: 1302.6445 · v2 · submitted 2013-02-26 · 🧮 math.NT · hep-th

Recognition: unknown

Graphical functions and single-valued multiple polylogarithms

Authors on Pith no claims yet
classification 🧮 math.NT hep-th
keywords functionsperiodsgraphicalmultiplepolylogarithmssingle-valuedcalculatefeynman
0
0 comments X
read the original abstract

Graphical functions are single-valued complex functions which arise from Feynman amplitudes. We study their properties and use their connection to multiple polylogarithms to calculate Feynman periods. For the zig-zag and two more families of phi^4 periods we give exact results modulo products. These periods are proved to be expressible as integer linear combinations of single-valued multiple polylogarithms evaluated at one. For the larger family of 'constructible' graphs we give an algorithm that allows one to calculate their periods by computer algebra. The theory of graphical functions is used to prove the zig-zag conjecture.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. The OPE Approach to Renormalization: Operator Mixing

    hep-th 2026-04 unverdicted novelty 7.0

    OPE-based recursive renormalization for mixed composite operators gives five-loop anomalous dimensions in phi^4 and two-loop in phi^3 models.

  2. Four-loop Anomalous Dimensions of Scalar-QED Theory from Operator Product Expansion

    hep-th 2026-04 unverdicted novelty 6.0

    Four-loop anomalous dimension of φ^Q in scalar-QED computed via OPE, extending prior three-loop results and validating the method in a gauge theory.

  3. Graphical Functions by Examples

    hep-th 2026-04 unverdicted novelty 2.0

    Graphical functions, defined as massless three-point position-space integrals, serve as a powerful tool for evaluating multi-loop Feynman integrals, with extensions to conformal field theory and recent algorithmic com...