Boundary conditions for massless excitations of a vortex and induced lower-dimensional gauge theory

We examine bosonic zero modes of a vortex in the abelian Higgs model in N dimensions. In the low-energy limit these modes induce some gauge theory of exactly massless vector and scalar fields in N-2 dimensions. The scalar and vector fields are connected with the broken translations and rotations in vacuum, respectively. Careful analysis of the boundary conditions needs to prove the existence of the gauge field. The symmetry of the lower-dimensional theory is broken by nonperturbative effects at a naturally small mass scale. (orig.)