Large Screening in Two Dimensional Nonabelian Vortex Systems

We study charge screening in a system of two dimensional nonabelian vortices, at finite temperature. Such vortices are generated after an $SO(3)$ global symmetry group is spontaneously broken to a discrete subgroup $\IQ_8$, where the latter is isomorphic to the nonabelian group of quaternions. Poisson-Boltzmann like equations are derived for the various inter-vortex potentials, and the solutions to lowest order in a small fugacity expansion, are shown to behave much like those in abelian or Coulomb charge systems. The consequences for the phase structure of the system are discussed, where the fugacities associated to the thermal production of the various types of nonabelian vortices, are shown to play a key role.