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arXiv · 2207.14806

Properties of the Conformal Yangian in Scalar and Gauge Field Theories

Nikolaos Dokmetzoglou·Louise Dolan
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Abstract

Properties of the SO(2,n) Yangian acting on scalar and gauge fields are presented. This differential operator representation of the infinite-dimensional extension of the conformal algebra SO(2,n) is proved to satisfy the Serre relation for arbitrary spacetime dimension n for off-shell scalar theory, but only on shell and for n=4 in the gauge theory. The SO(2,n) Yangian acts simply on the off-shell kinematic invariants $(k_I+k_{I+1}+ ...)^2$, and it annihilates individual off-shell scalar $\lambda \phi^3$ Feynman tree graphs for n=6 if the differential operator representation is extended by graph dependent evaluation terms. The SO(2,4) Yangian level one generators are shown to act in a compact way on pure Yang-Mills gluon tree amplitudes. The action of the Yangian on the scattering polynomials of a CHY formalism is also described.

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Nikolaos Dokmetzoglou, Louise Dolan. 2022-07-29. Properties of the Conformal Yangian in Scalar and Gauge Field Theories. https://doi.org/10.1007/jhep02(2023)137

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