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Recursive computation of Feynman periods

  • Regular Article - Theoretical Physics
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  • Published: 30 August 2022
  • volume 2022, Article number: 291 (2022)
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Recursive computation of Feynman periods
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  • Michael Borinsky  ORCID: orcid.org/0000-0002-0581-32761 &
  • Oliver Schnetz2 

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A preprint version of the article is available at arXiv.

Abstract

Feynman periods are Feynman integrals that do not depend on external kinematics. Their computation, which is necessary for many applications of quantum field theory, is greatly facilitated by graphical functions or the equivalent conformal four-point integrals. We describe a set of transformation rules that act on such functions and allow their recursive computation in arbitrary even dimensions. As a concrete example we compute all subdivergence-free Feynman periods in ϕ3 theory up to six loops and 561 of 607 Feynman periods at seven loops analytically. Our results support the conjectured existence of a coaction structure in quantum field theory and suggest that ϕ3 and ϕ4 theory share the same number content.

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Authors and Affiliations

  1. Institute for Theoretical Studies, ETH Zürich, Rämistrasse 101, 8092, Zürich, Switzerland

    Michael Borinsky

  2. Department Mathematik, Friedrich Alexander Universität, Cauerstraße 11, 91058, Erlangen, Germany

    Oliver Schnetz

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  1. Michael Borinsky
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  2. Oliver Schnetz
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Correspondence to Michael Borinsky.

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Borinsky, M., Schnetz, O. Recursive computation of Feynman periods. J. High Energ. Phys. 2022, 291 (2022). https://doi.org/10.1007/JHEP08(2022)291

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  • Received: 22 June 2022

  • Revised: 25 July 2022

  • Accepted: 27 July 2022

  • Published: 30 August 2022

  • DOI: https://doi.org/10.1007/JHEP08(2022)291

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Keywords

  • Field Theories in Higher Dimensions
  • Differential and Algebraic Geometry
  • Renormalization and Regularization
  • Renormalization Group
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