  Results ranging from Ashtekar variables to the perturbative
Bern-Carrasco-Johansson (BCJ) double copy suggest a deep relation between
Yang-Mills theory and Einstein gravity. I examine this relation by writing down
the tetradic Palatini action for Einstein gravity and covariantly decomposing
its variables into two $SL(2,\mathbb{C})$ connections and two soldering forms.
This leads to a conjecture that the BCJ double copy can be understood through a
"holomorphic trail", a series of injection maps between two copies of $SU(2)$
theories and Einstein gravity.
