  Different models of field theories in two dimensions can be described by the
action $Tr\int \vf F$. In the presence of a curved background, we construct a
local supersymmetry-like transformations under which the action is invariant.
Furthermore, by analysing the cohomology of the theory we show the absence of
anomalies. Also the ultraviolet as well as the infrared finiteness of the
theory are proven to all orders of perturbation theory.
