  Liquid crystals inevitably possess topological defect excitations generated
through boundary conditions, applied fields or in quenches to the ordered
phase. In equilibrium pairs of defects coarsen and annihilate as the uniform
ground state is approached. Here we show that defects in active liquid crystals
exhibit profoundly different behavior, depending on the degree of activity and
its contractile or extensile character. While contractile systems enhance the
annihilation dynamics of passive systems, extensile systems act to drive
defects apart so that they swarm around in the manner of topologically
well-characterized self-propelled particles. We develop a simple analytical
model for the defect dynamics which reproduces the key features of both the
numerical solutions and recent experiments on microtuble-kinesin assemblies.
