Yang-Mills sources in biconformal gravity

Understand

Biconformal gravity, based on gauging of the conformal group to 2n dimensions, reproduces n-dim scale-covariant general relativity on the co-tangent bundle in any dimension.

• We generalize this result to include Yang-Mills matter sources formulated as SU\left(N\right) gauge theories with a twisted action on the full 2n-dimensional biconformal space.
• We show that the coupling of the sources to gravity does not stop the reduction of effective dimension 2n\rightarrow n of the gravity theory, and instead forces the Yang-Mills source to reduce to ordinary n-dimensional Yang-Mills theory on the gravitating cotangent bundle, with the usual Yang-Mills energy tensor as gravitational source.
• The results apply as well to gravity with sources on K\"ahler manifolds and in double field theories.