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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2412.19296 |
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| _version_ | 1866912170330030080 |
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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 |