  In this work we use constructs from the dual space of the semi-direct product
of the Virasoro algebra and the affine Lie algebra of a circle to write a
theory of gravitation which is a natural analogue of Yang-Mills theory. The
theory provides a relation between quadratic differentials in 1+1 dimensions
and rank two symmetric tensors in higher dimensions as well as a covariant
local Lagrangian for two dimensional gravity. The isotropy equations of
coadjoint orbits are interpreted as Gauss law constraints for a field theory in
two dimensions, which enables us to extend to higher dimensions. The theory has
a Newtonian limit in any space-time dimension. Our approach introduces a novel
relationship between string theories and 2D field theories that might be useful
in defining dual theories. We briefly discuss how this gravitational field
couples to fermions.
