Geometry and dynamics of a coupled 4D-2D quantum field theory

A bstract Geometric and dynamical aspects of a coupled 4 D -2 D interacting quantum field theory — the gauged nonAbelian vortex — are investigated. The fluctuations of the internal 2 D nonAbelian vortex zeromodes excite the massless 4 D Yang-Mills modes and in general give rise to divergent energies. This means that the well-known 2 D ℂ ℙ N − 1 zeromodes associated with a nonAbelian vortex become nonnormalizable. Moreover, all sorts of global, topological 4 D effects such as the nonAbelian Aharonov-Bohm effect come into play. These topological global features and the dynamical properties associated with the fluctuation of the 2 D vortex moduli modes are intimately correlated, as shown concretely here in a U 0 (1) × SU l ( N ) × SU r ( N ) model with scalar fields in a bifundamental representation of the two SU( N ) factor gauge groups.