  Marginal operators in a $d$-dimensional conformal field theory (CFT), those
with conformal dimension $\Delta=d$, give us information about the space of
related theories. This can be incredibly useful when trying to develop an
intrinsic definition of a holographic CFT. Recent work has established that in
the case of celestial CFTs, those dual to asymptotically flat spacetimes,
marginal operators can be constructed as shadow transforms of soft scalars. In
this work, rather than starting from a bulk theory of scalars, we start with
Yang-Mills and construct marginal operators from soft gluons via light
transforms and a new set of transformations called half-shadow transforms. We
obtain the local metric and connections for the associated conformal manifold
by studying the two- and three-point functions of these marginal operators. We
then discuss the implications of this for broadening our understanding of
operator product expansions of soft operators in celestial CFTs.
