  It is known that a source-free Yang-Mills theory with the normal conformal
Cartan connection used as the gauge potential gives rise to equations of motion
equivalent to the vanishing of the Bach tensor. We investigate the conformally
invariant presymplectic potential current obtained from this theory and find
that on the solutions to the Einstein field equations, it can be decomposed
into a topological term derived from the Euler density and a part proportional
to the potential of the standard Einstein-Hilbert Lagrangian. The pullback of
our potential to the asymptotic boundary of asymptotically de Sitter spacetimes
turns out to coincide with the current obtained from the holographically
renormalized gravitational action. This provides an alternative derivation of a
symplectic structure on scri without resorting to holographic techniques. We
also calculate our current at the null infinity of asymptotically flat
spacetimes and in particular show that it vanishes for variations induced by
the BMS symmetries. In addition, we calculate the Noether currents and charges
corresponding to gauge transformations and diffeomorphisms.
