Downward shift of infrared conductivity spectral weight at the DDW transition: role of anisotropy

We consider the motion of conductivity spectral weight at a finite-temperature phase transition at which $d_{x^2-y^2}$ density-wave (DDW) order develops. We show that there is a shift of spectral weight to higher frequencies if the quasiparticle lifetime is assumed to be isotropic, but a shift to lower frequencies if the quasiparticle lifetime is assumed to be anisotropic. We suggest that this is consistent with recent experiments on the pseudogap phase of the cuprate superconductors and, therefore, conclude that the observation of a downward shift in the spectral weight at the pseudogap temperature does not militate against the DDW theory of the pseudogap.