TOPOLOGY AND NEMATIC ORDERING .1. A GAUGE-THEORY

We consider the weakly first-order phase transition between the isotro pic and ordered phases of nematic liquid crystals in terms of the beha vior of topological line defects. Analytical and Monte Carlo results a re presented for a recently introduced coarse-grained lattice theory o f nematics that incorporates nematic inversion symmetry as a local gau ge invariance. The nematic-isotropic transition becomes more weakly fi rst order as the disclination core energy is increased, eventually spl itting into two continuous transitions involving the unbinding and con densation of defects, respectively. These transitions are shown to be in the Ising and Heisenberg universality classes. A novel isotropic ph ase with topological order occurs between them.