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Yangian Bootstrap for Massive Feynman Integrals

by Florian Loebbert, Julian Miczajka, Dennis Müller, Hagen Münkler

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Florian Loebbert · Julian Miczajka · Dennis Müller · Hagen Münkler
Submission information
Preprint Link: scipost_202011_00017v2  (pdf)
Date accepted: 2021-07-02
Date submitted: 2021-05-12 22:51
Submitted by: Miczajka, Julian
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Mathematical Physics
  • High-Energy Physics - Theory
Approach: Theoretical


We extend the study of the recently discovered Yangian symmetry of massive Feynman integrals and its relation to massive momentum space conformal symmetry. After proving the symmetry statements in detail at one and two loop orders, we employ the conformal and Yangian constraints to bootstrap various one-loop examples of massive Feynman integrals. In particular, we explore the interplay between Yangian symmetry and hypergeometric expressions of the considered integrals. Based on these examples we conjecture single series representations for all dual conformal one-loop integrals in $D$ spacetime dimensions with generic massive propagators.

List of changes

- Added footnote 3 above (3.2).
- Added footnote 4 above (3.20).
- Added sentence "Notably, all integrals at higher loops that are expected to be Yangian invariant are related to planar diagrams. At this point there is no evidence that the Yangian symmetry of single Feynman diagrams can be generalized beyond planar integrals." at the end of section 3.2.
- Added footnote 6 on page 19.
- Added sentence "These constraints can come from e.g.\ permutation symmetry or kinematic limits that simplify the form of the integral, such as sending a mass to zero or an external point to infinity." to item 5 in section 4.2.
- Fixed a typo on page 26 (repetition "to to").
- Fixed a type in equation (7.9).

Published as SciPost Phys. 11, 010 (2021)

Reports on this Submission

Anonymous Report 2 on 2021-6-29 (Invited Report)


The authors have addressed all the points made in the original report. I am happy to recommend publication.

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Anonymous Report 1 on 2021-6-28 (Invited Report)


I thank the authors for adding sentences along the lines of my suggestions. I recommend publication of the manuscript in its current form.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

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