Geometric and dynamical aspects of a coupled 4D-2D interacting quantum field theory - the gauged nonAbelian vortex will be discussed. The fluctuations of the internal 2D nonAbelian vortex zeromodes excite the massless 4D Yang-Mills modes, which give rise to divergent energies. This means that the well-known 2D CP(N-1) zeromodes associated with a nonAbelian vortex become nonnormalizable. At the same time, all sorts of global, topological 4D effects such as the nonAbelian Aharonov-Bohm effect come into play. These topological, global features and the dynamical properties of the fluctuations of the 2D vortex moduli are intimately correlated, as shown concretely here in a U(1) xSU(N) x SU(N) model with scalar fields in a bifundamental representation of the two SU(N) factor gauge groups.