  We consider a collection of self-driven apolar particles on a substrate that
organize into an active nematic phase at sufficiently high density or low
noise. Using the dynamical renormalization group, we systematically study the
2d fluctuating ordered phase in a coarse-grained hydrodynamic description
involving both the nematic director and the conserved density field. In the
presence of noise, we show that the system always displays only quasi-long
ranged orientational order beyond a crossover scale. A careful analysis of the
nonlinearities permitted by symmetry reveals that activity is dangerously
irrelevant over the linearized description, allowing giant number fluctuations
to persist though now with strong finite-size effects and a non-universal
scaling exponent. Nonlinear effects from the active currents lead to power law
correlations in the density field thereby preventing macroscopic phase
separation in the thermodynamic limit.
