  The requirement of diffeomorphism symmetry for the target space can lead to
anomalous commutators for the energy-momentum tensor for sigma models and for
fluid dynamics, if certain topological terms are added to the action. We
analyze several examples . A particular topological term is shown to lead to
the known effective hydrodynamics of a dense collection of vortices, i.e. the
vortex fluid theory in 2+1 dimensions. The possibility of a similar vortex
fluid in 3+1 dimensions, as well as a fluid of knots and links, with possible
extended diffeomorphism algebras is also discussed.
