  Recent experiments and numerical studies have drawn attention to the dynamics
of active nematics. Two-dimensional active nematics flow spontaneously and
exhibit spatiotemporal chaotic flows with proliferation of topological defects
in the nematic texture. It has been proposed that the dynamics of active
nematics can be understood in terms of the dynamics of interacting defects,
propelled by active stress. Previous work has derived effective equations of
motion for individual defects as quasi-particles moving in the mean field
generated by other defects, but an effective theory governing multi-defect
dynamics has remained out of reach. In this paper, we examine the dynamics of
2D active nematics in the limit of strong order and overdamped compressible
flow. The activity-induced defect dynamics is formulated as a perturbation of
the manifold of quasi-static nematic textures explicitly parameterized by
defect positions. This makes it possible to derive a set of coupled ordinary
differential equations governing defect (and therefore texture) dynamics.
Interestingly, because of the non-orthogonality of textures associated with
individual defects, their motion is coupled through a position dependent
``collective mobility" matrix. In addition to the familiar active
self-propulsion of the $+1/2$ defect, we obtain new collective effects of
activity that can be interpreted in terms of non-central and non-reciprocal
interactions between defects.
