City Research Online

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.

Publication Type:	Article
Additional Information:	© The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Publisher Keywords:	Integrable Field Theories, Scattering Amplitudes
Subjects:	Q Science > QC Physics
Departments:	School of Science & Technology School of Science & Technology > Department of Mathematics
SWORD Depositor:	Symplectic Administrator

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