  We formulate the statistical dynamics of topological defects in the active
nematic phase, formed in two dimensions by a collection of self-driven
particles on a substrate. An important consequence of the non-equilibrium drive
is the spontaneous motility of strength +1/2 disclinations. Starting from the
hydrodynamic equations of active nematics, we derive an interacting particle
description of defects that includes active torques. We show that activity,
within perturbation theory, lowers the defect-unbinding transition temperature,
determining a critical line in the temperature-activity plane that separates
the quasi-long-range ordered (nematic) and disordered (isotropic) phases. Below
a critical activity, defects remain bound as rotational noise decorrelates the
directed dynamics of +1/2 defects, stabilizing the quasi-long-range ordered
nematic state. This activity threshold vanishes at low temperature, leading to
a re-entrant transition. At large enough activity, active forces always exceed
thermal ones and the perturbative result fails, suggesting that in this regime
activity will always disorder the system. Crucially, rotational diffusion being
a two-dimensional phenomenon, defect unbinding cannot be described by a
simplified one-dimensional model.
