Abstract
We study celestial amplitudes in (super) Yang-Mills theory using a parameterisation of the spinor helicity variables where their overall phase is not fixed by the little group action. In this approach the spin constraint $h-\bar{h}=J$ for celestial conformal primaries emerges naturally from a new Mellin transform, and the action of conformal transformations on celestial amplitudes is derived. Applying this approach to $\mathcal{N}\!=\!4$ super Yang-Mills, we show how the appropriate definition of on-shell superspace coordinates leads naturally to a formulation of chiral celestial superamplitudes and a representation of the generators of the four-dimensional superconformal algebra on the celestial sphere, which by construction annihilate all tree-level celestial superamplitudes.
Highlights
The quest for secret symmetries of the S-matrix of gauge theory and gravity has been a continuous source of surprises
An example is the discovery of the dual superconformal symmetry of N 1⁄4 4 supersymmetric Yang-Mills (SYM) theory, first conjectured in [1] and subsequently proved at tree level in [2]
It emerged from earlier studies of iterative structures of maximally helicity violating (MHV) amplitudes in perturbation theory [3,4,5] and at strong coupling [6]
Summary
The quest for secret symmetries of the S-matrix of gauge theory and gravity has been a continuous source of surprises. The work of [10,11,12] suggested a new way to interpret scattering amplitudes of a generic fourdimensional theory as correlators of a two-dimensional conformal field theory living at null infinity of Minkowski spacetime, known as the celestial sphere. In order to answer this question in a systematic way, in particular ensuring that the new generators in celestial space naturally obey the superconformal algebra, we find it useful to introduce a new “chiral” Mellin transform In this approach we define the Mellin transform to celestial space in terms of standard spinor helicity variables without modding out the little group redundancy occurring in the expression of a null momentum in terms of spinor variables. The Appendix expands on the derivation of weights of celestial operators, and in particular we present in Table I the list of weights of all relevant celestial operators
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