  Coadjoint orbits of the Virasoro and Kac-Moody algebras provide geometric
actions for matter coupled to gravity and gauge fields in two dimensions.
However, the Gauss' law constraints that arise from these actions are not
necessarily endemic to two-dimensional topologies. Indeed the constraints
associated with Yang-Mills naturally arise from the coadjoint orbit
construction of the WZW model. One may in fact use a Yang-Mills theory to
provide dynamics to the otherwise fixed coadjoint vectors that define the
orbits. In this letter we would like to exhibit an analogue of the Yang-Mills
classical action for the diffeomorphism sector. With this analogue one may
postulate a 4D theory of gravitation that is related to an underlying two
dimensional theory. Instead of quadratic differentials, a (1,3) pseudo tensor
becomes the dynamical variable. We briefly discuss how this tensor may be
classically coupled to matter.
