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arxiv: 2105.05015 · v3 · pith:ZQMY3EOFnew · submitted 2021-05-11 · ✦ hep-th · math-ph· math.MP

Graphical functions in even dimensions

classification ✦ hep-th math-phmath.MP
keywords functionsgraphicaltheorydimensionsevenfeynmanlooporders
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Graphical functions are special position space Feynman integrals, which can be used to calculate Feynman periods and one- or two-scale processes at high loop orders. With graphical functions, renormalization constants have been calculated to loop orders seven and eight in four-dimensional $\phi^4$ theory and to order five in six-dimensional $\phi^3$ theory. In this article we present the theory of graphical functions in even dimensions $\geq4$ with detailed reviews of known properties and full proofs whenever possible.

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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...