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We present a discrete basis of solutions of the massless Klein-Gordon equation in 3 + 1 Minkowski space which transform as 𝔰𝔩(2, ℂ) Lorentz/conformal primaries and descendants, and whose elements all have integer conformal dimension. We show that the basis is complete in the sense that the Wightman function can be expressed as a quadratic sum over the basis elements.more » « less
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Crawley, Erin; Miller, Noah; Narayanan, Sruthi A.; Strominger, Andrew (, Journal of High Energy Physics)A bstract The bulk-to-boundary dictionary for 4D celestial holography is given a new entry defining 2D boundary states living on oriented circles on the celestial sphere. The states are constructed using the 2D CFT state-operator correspondence from operator insertions corresponding to either incoming or outgoing particles which cross the celestial sphere inside the circle. The BPZ construction is applied to give an inner product on such states whose associated bulk adjoints are shown to involve a shadow transform. Scattering amplitudes are then given by BPZ inner products between states living on the same circle but with opposite orientations. 2D boundary states are found to encode the same information as their 4D bulk counterparts, but organized in a radically different manner.more » « less