Conductivity sum rule, implication for in-plane dynamics, and c-axis response

Recently observed c-axis optical sum rule violations indicate non-Fermi-liq uid in-plane behavior. For coherent c-axis coupling, the observed flat, nea rly frequency-independent c-axis conductivity sigma(1)(omega) implies a lar ge in-plane scattering rate Gamma around (0,pi) and therefore any pseudogap that might form at low frequency in the normal state will be smeared. On t he other hand, incoherent c-axis coupling places no restriction on the valu e of Gamma and gives a more consistent picture of the observed sum-rule vio lation which, we find in some cases, can be less than half.