  A new topological conformal field theory in four Euclidean dimensions is
constructed from N=4 super Yang-Mills theory by twisting the whole of the
conformal group with the whole of the R-symmetry group, resulting in a theory
that is conformally invariant and has two conformally invariant BRST operators.
A curved space generalisation is found on any Riemannian 4-fold. This
formulation has local Weyl invariance and two Weyl-invariant BRST symmetries,
with an action and energy-momentum tensor that are BRST-exact. This theory is
expected to have a holographic dual in 5-dimensional de Sitter space.
