Kinematically constrained vortex dynamics in charge density waves

We build a minimal model of dissipative vortex dynamics in two spatial dimensions, subject to a kinematic constraint: dipole conservation. The additional conservation law implies anomalously slow decay rates for vortices. We argue that this model of vortex dynamics is relevant for a broad range of time scales during a quench into a uniaxial charge density wave state. Our predictions are consistent with recent experiments on uniaxial charge density wave formation in $\mathrm{LaTe}_3$.