The Pseudogap Challenge: Understanding the ab-Plane AC Conductivity below Tc

We establish that the cuprate pseudogap plays a crucial role in the $ab$-plane optical conductivity $\sigma(\omega,T)$ for temperatures $T \le T_c$. The pseudogap signatures in $\sigma(\omega,T)$ associated with competing proposals of a ``hidden order'' and ``superconducting'' origin for the $d_{x^2 - y^2}$ pseudogap are found to differ in their qualitative $\omega,T$ dependences. For the latter case, as $T$ increases from 0, excess low $\omega$ weight appears; moreover, a much wider range of $\omega$ contributes to form the condensate. We discuss these theories in light of current experiments.