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Integrability for Feynman Integrals
by Florian Loebbert
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Submission summary
| Authors (as registered SciPost users): | Florian Loebbert |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202212_00046v1 (pdf) |
| Date submitted: | 2022-12-18 18:19 |
| Submitted by: | Loebbert, Florian |
| Submitted to: | SciPost Physics Proceedings |
| Proceedings issue: | 34th International Colloquium on Group Theoretical Methods in Physics (GROUP2022) |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We give a brief overview of the Yangian symmetry of Feynman integrals. After a short intro- duction to the Yangian and integrability, we motivate the emergence of integrable structures for Feynman integrals via the fishnet limit of AdS/CFT. We discuss the resulting Yangian differential equations for massless fishnets in four dimensions as well as generalizations to massive propagators and generic dimensions. We also comment on the relation to momentum space conformal symmetry and on examples in dimensional regularization. Finally we sketch the recent application to fishnet integrals in two spacetime dimensions and the curious identification of Yangian invariants with period integrals of Calabi-Yau geometries.
Current status:
Reports on this Submission
Anonymous Report 1 on 2023-2-2 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202212_00046v1, delivered 2023-02-02, doi: 10.21468/SciPost.Report.6664
Strengths
1 - Short and to the point
2 - Good amount of references
3 - Comprehensive
4 - Clear and fairly well written
Weaknesses
1 - Does not advance the field in any way
Report
The paper is a short account of the status of integrability and, in particular, the use of Yangian symmetry in the context of Quantum Field Theory and the evaluation of Feynman Diagrams.
While it does not advance the current knowledge on the subject in any way, it is still a very useful and nice account, collecting together information which is often scattered and giving a number of references.
Requested changes
1 - Pag 3: "The Yangian has been studied in the context of various physical setups; [...]". I would suggest the author to provide references for the examples he mentions.