Properties of the Conformal Yangian in Scalar and Gauge Field Theories

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 $(k_I+k_{I+1}+\mathrm{.}\mathrm{.}\mathrm{.}{)}^2$, 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.