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arXiv · 2412.19296

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

Fedor Levkovich-Maslyuk·Victor Mishnyakov
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Abstract

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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Fedor Levkovich-Maslyuk, Victor Mishnyakov. 2024-12-26. Yangian symmetry, GKZ equations and integrable Feynman graphs in conformal variables. https://arxiv.org/abs/2412.19296

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