Integrability and volume-preserving diffeomorphisms
We construct a class of field theories which are either integrable or contain integrable subsectors defined by additional constraints. Here integrability means the existence of infinitely many conservation laws. These theories have three-dimensional target space, like the Skyrme model, and their infinitely many conserved currents turn out to be Noether currents of the volume-preserving diffeomorphisms on target space. Further, we discuss applications to some specific field theories.