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Hauptverfasser: Levkovich-Maslyuk, Fedor, Mishnyakov, Victor
Format: Preprint
Veröffentlicht: 2024
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Online-Zugang:https://arxiv.org/abs/2412.19296
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author Levkovich-Maslyuk, Fedor
Mishnyakov, Victor
author_facet Levkovich-Maslyuk, Fedor
Mishnyakov, Victor
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2412_19296
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Yangian symmetry, GKZ equations and integrable Feynman graphs in conformal variables
Levkovich-Maslyuk, Fedor
Mishnyakov, Victor
High Energy Physics - Theory
Mathematical Physics
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.
title Yangian symmetry, GKZ equations and integrable Feynman graphs in conformal variables
topic High Energy Physics - Theory
Mathematical Physics
url https://arxiv.org/abs/2412.19296