Properties of the Conformal Yangian in Scalar and Gauge Field Theories

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 $\lambda {\varphi }^3$ 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.

38 pages

References in corpus (6)

• New Relations for Gauge-Theory Amplitudes
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Lectures on Yangian Symmetry
• One-loop Correlators and BCJ Numerators from Forward Limits
• Yangian Bootstrap for Massive Feynman Integrals
• Off-Shell CHY Amplitudes and Feynman Graphs

Cited by in corpus (2)

• Integrability for Feynman Integrals
• The Feyn-Structure of Yangian Symmetry