Work

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

Year: 2026

Type: article

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.

Source: Journal of High Energy Physics

DOI: 10.1007/jhep10(2026)220

Authors: Fedor Levkovich-Maslyuk, Victor Mishnyakov

Institutions: City St George's, University of London, Stockholm University, KTH Royal Institute of Technology

Language: English

Topic: Black Holes and Theoretical Physics

Subfield: Nuclear and High Energy Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: diamond

Funders: NordForsk, Science and Technology Facilities Council

Award: G4917226169