State-Operator Correspondence in Celestial Conformal Field Theory

TL;DR

This paper develops a new boundary state-operator correspondence in 4D celestial holography, linking bulk scattering data to 2D boundary states on the celestial sphere using CFT techniques.

Contribution

It introduces a novel boundary state construction in celestial CFT, utilizing the BPZ framework and shadow transforms to relate 4D scattering amplitudes to 2D boundary states.

Findings

Boundary states encode 4D bulk information in 2D CFT form.

Scattering amplitudes are expressed as BPZ inner products of boundary states.

Shadow transforms relate bulk adjoints to boundary state inner products.

Abstract

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.