Topological properties of linked disclinations in anisotropic liquids

Abstract

A connection between the topological properties of the O(3) and SO(3)- sigma models based on Hopf's invariant and the Wess-Zumino term, respectively, and related topological concepts are indicated. This is applied to the O(3)/Z2- and the SO(3)/Pi- sigma models, where Z2 and PiC SO(3) are point symmetry groups describing anisotropic liquids. It is shown that the Hopf invariant for the nematic liquid assumes integer multiples of 1/4 and similar results hold for the other sigma -models. Applications to a topological field theory of O(3)/Z2- and SO(3)/Pi- sigma models are indicated.