Renormalizability of a mofified generally covariant Yang-Mills action

A modified generally covariant Yang-Mills action, which depends on the complex structure of spacetime and not its metric, is proved to be renormalizable. This proof makes this Lagrangian model the unique known generally covariant four dimensional model to be renormalizable without higher order derivatives. The first order one-loop diagrams are computed in an appropriate gauge condition and they are found to be finite.