  A framework for constructing new kinds of gauge theories is suggested.
Essentially it consists in replacing Lie algebras by Lie or Courant algebroids.
Besides presenting novel topological theories defined in arbitrary spacetime
dimensions, we show that equipping Lie algebroids E with a fiber metric having
sufficiently many E-Killing vectors leads to an astonishingly mild deformation
of ordinary Yang-Mills theories: Additional fields turn out to carry no
propagating modes. Instead they serve as moduli parameters gluing together in
part different Yang-Mills theories. This leads to a symmetry enhancement at
critical points of these fields, as is also typical for String effective field
theories.
