Existence of the massive SO(3) vortices

In the massive SO(3) gauge field theory, a critical choice of the configuration ansatz leads to a system of the Bogomol'nyi type equations governing the unstable modes of the model. A 't Hooft periodic condition implies the quantization of the flux lines confined in a cell domain if a certain class of solutions exist. The present paper establishes an existence theorem for such solutions via a constrained variational principle. These solutions exhibit the analogous properties of the vortex-like solutions predicted in the theory of type II superconductivity by Abrikosov.