  Developing on the ideas of R. Stora and coworkers, a formulation of two
dimensional field theory endowed with extended conformal symmetry is given,
which is based on deformation theory of holomorphic and Hermitian spaces. The
geometric background consists of a vector bundle $E$ over a closed surface
$\Sigma$ endowed with a holomorphic structure and a Hermitian structure
subordinated to it. The symmetry group is the semidirect product of the
automorphism group ${\rm Aut}(E)$ of $E$ and the extended Weyl group ${\rm
Weyl}(E)$ of $E$ and acts on the holomorphic and Hermitian structures. The
extended Weyl anomaly can be shifted into an automorphism chirally split
anomaly by adding to the action a local counterterm, as in ordinary conformal
field theory. The dependence on the scale of the metric on the fiber of $E$ is
encoded in the Donaldson action, a vector bundle generalization of the
Liouville action. The Weyl and automorphism anomaly split into two
contributions corresponding respectively to the determinant and
projectivization of $E$. The determinant part induces an effective ordinary
Weyl or diffeomorphism anomaly and the induced central charge can be computed.
