Stephan Stieberger (München): Elements of Celestial Conformal Field Theory

I will introduce into subject of holographic description of four-dimensional massless physics as conformal field theory on the celestial sphere and report on progress on celestial conformal field theory (CCFT). In celestial holography, four-dimensional scattering amplitudes are considered as two-dimensional conformal correlators of a putative two-dimensional CCFT.
The simplest way of converting momentum space amplitudes into CCFT correlators is by taking their Mellin transforms with respect to light-cone energies. For massless particles, like gluons, however, such a construction leads to three-point and four-point correlators that vanish everywhere except for a measure zero hypersurface of celestial coordinates.
This is due to the four-dimensional momentum conservation law that constrains the insertion points of the operators associated with massless particles. These correlators are reminiscent of Coulomb gas correlators that, in the absence of background charges, vanish due to charge conservation.
We supply the background momentum by coupling Yang-Mills theory to a background dilaton field, with the (complex) dilaton source localized on the celestial sphere.
We show that the celestial Yang-Mills amplitudes evaluated in the presence of a spherical dilaton shockwave are given by the correlation functions of primary field operators factorized into the holomorphic current operators times the "light" Liouville operators. They are evaluated in the semiclassical limit of Liouville theory (the limit of infinite central charge) and are determined by the classical Liouville field describing metrics on the celestial sphere.