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Peer-reviewedCC BY 4.0Journal of High Energy Physics

Yangian symmetry, GKZ equations and integrable Feynman graphs in conformal variables

  • Fedor Levkovich-Maslyuk1
  • Victor Mishnyakov2
  1. 1City St George’s, University of London
  2. 2Nordita, KTH Royal Institute of Technology and Stockholm University
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Abstract

A bstract : We study the differential equations that follow from Yangian symmetry which was recently observed for a large class of conformal Feynman graphs, originating from integrable ‘fishnet’ theories. We derive, for the first time, the explicit general form of these equations in the most useful conformal cross-ratio variables, valid for any spacetime dimension. This allows us to explore their properties in detail. In particular, we observe that for general Feynman graphs a large set of terms in the Yangian equations can be identified with famous GKZ (Gelfand-Kapranov-Zelevinsky) hypergeometric operators. We also show that for certain nontrivial graphs the relation with GKZ systems is exact, opening the way to using new powerful solution methods. As a side result, we also elucidate the constraints on the topology and parameter space of Feynman graphs stemming from Yangian invariance.

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Cite

BibTeXRIS
BibTeX
@article{levkovichmaslyuk2026yangian,
  title = {{Yangian symmetry, GKZ equations and integrable Feynman graphs in conformal variables}},
  author = {Fedor Levkovich-Maslyuk and Victor Mishnyakov},
  journal = {Journal of High Energy Physics},
  year = {2026},
  month = oct,
  doi = {10.1007/jhep10(2026)220},
  url = {https://link.springer.com/article/10.1007/JHEP10(2026)220},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Yangian symmetry, GKZ equations and integrable Feynman graphs in conformal variables
AU  - Fedor Levkovich-Maslyuk
AU  - Victor Mishnyakov
PY  - 2026
DA  - 2026/10/21
JO  - Journal of High Energy Physics
DO  - 10.1007/jhep10(2026)220
UR  - https://link.springer.com/article/10.1007/JHEP10(2026)220
AB  - A bstract : We study the differential equations that follow from Yangian symmetry which was recently observed for a large class of conformal Feynman graphs, originating from integrable ‘fishnet’ theories. We derive, for the first time, the explicit general form of these equations in the most useful conformal cross-ratio variables, valid for any spacetime dimension. This allows us to explore their properties in detail. In particular, we observe that for general Feynman graphs a large set of terms in the Yangian equations can be identified with famous GKZ (Gelfand-Kapranov-Zelevinsky) hypergeometric operators. We also show that for certain nontrivial graphs the relation with GKZ systems is exact, opening the way to using new powerful solution methods. As a side result, we also elucidate the constraints on the topology and parameter space of Feynman graphs stemming from Yangian invariance.
SN  - 1029-8479
ER  -