Title: Conformal Yangian and Tree Amplitudes in Scalar and Gauge Field Theories

Abstract: Scattering amplitudes are intimately related to both experimental and theoretical ongoing efforts of testing the Standard Model of particle physics and our understanding of quantum field theory at large, through their computation to higher orders of precision and the study of their often unexpected and fascinating mathematical properties. It is within this latter field of study that our research lies. We investigate the infinite-dimensional Yangian extension of the conformal algebra so(2,n), where n is the number of space-time dimensions, and its action on the tree-level scattering amplitudes of scalar ϕ3 theory and pure Yang-Mills theory. These two non-supersymmetric field theories are connected through the Cachazo-He-Yuan (CHY) scattering equations formalism. We first establish the consistency of the conformal Yangian algebra, Y[so(2,n)], for a differential operator representation of its generators in momentum-space. We prove that this representation satisfies the Serre relation, off-shell and in any number of space-time dimensions n for scalar fields, but only on-shell and in n=4 space-time dimensions for spin-one gauge fields. We then show that the conformal Yangian generators annihilate individual off-shell scalar ϕ3 Feynman tree graphs in n=6 dimensions when the differential operator representation of Y[so(2,n)] is extended by graph-specific so-called evaluation parameter terms. We further show that the action of the conformal Yangian generators on the on-shell three-point and four-point pure Yang-Mills theory gluon tree amplitudes has a compact, albeit non-vanishing, form in n=4 dimensions. We conclude our investigation by exploring the action of the Y[so(2,n)] generators on the off-shell scattering polynomials of the CHY formalism relating the two theories.

Nikos Dokmetzoglou

Time: May 8, 2023 10:00 AM Eastern Time (US and Canada)

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