Screening in two-dimensional non-abelian vortex systems

Abstract We study charge screening in a system of two-dimensional non-abelian vortices, at finite temperature. Such vortices are generated after an SO(3) global symmetry group is spontaneously broken to a discrete subgroup Q 8 , where the latter is isomorphic to the non-abelian group of quatemions. 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 non-abelian vortices, are shown to play a key role.