  In celestial holography, four-dimensional scattering amplitudes are
considered as two-dimensional conformal correlators of a putative
two-dimensional celestial conformal field theory (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. This picture emerges from the
physical interpretation of the solutions of the system of differential
equations discovered by Banerjee and Ghosh. We show that the solutions can be
written as Mellin transforms of the amplitudes evaluated in such a dilaton
background. The resultant three-gluon and four-gluon amplitudes are
single-valued functions of celestial coordinates enjoying crossing symmetry and
all other properties expected from standard CFT correlators. We use them to
extract OPEs and compare them with the OPEs extracted from multi-gluon
celestial amplitudes without a dilaton background. We perform the conformal
block decomposition of the four-gluon single-valued correlator and determine
the dimensions, spin and group representations of the entire primary field
spectrum of the Yang-Mills sector of CCFT.
