Properties of the Conformal Yangian in Scalar and Gauge Field Theories

TL;DR

This paper explores the properties of the SO(2,n) Yangian symmetry in scalar and gauge field theories, revealing its differential operator representation, conditions for satisfying Serre relations, and its action on scattering amplitudes and invariants.

Contribution

It demonstrates the differential operator representation of the SO(2,n) Yangian satisfies Serre relations in scalar theories and describes its action on scattering amplitudes in gauge theories.

Findings

Yangian acts on off-shell scalar invariants and annihilates certain Feynman graphs.

Yangian generators act compactly on Yang-Mills gluon tree amplitudes.

Yangian action on CHY scattering polynomials is characterized.

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.