  Recent microwave conductivity measurements of detwinned, high-purity,
slightly overdoped YBa$_{2}$Cu$_{3}$O$_{6.993}$ crystals reveal a linear
temperature dependence and a near-Drude lineshape for temperatures between 1
and 20 K and frequencies ranging from 1 to 75 GHz. Prior theoretical work has
shown that simple models of scattering by point defects (impurities) in d-wave
superconductors are inconsistent with these results. It has therefore been
suggested that scattering by extended defects such as twin boundary remnants,
left over from the detwinning process, may also be important. We calculate the
self-energy and microwave conductivity in the self-consistent Born
approximation (including vertex corrections) for a d-wave superconductor in the
presence of scattering from extended linear defects. We find that in the
experimentally relevant limit ($\Omega, 1/\tau \ll T \ll \Delta_{0}$), the
resulting microwave conductivity has a linear temperature dependence and a
near-Drude frequency dependence that agrees well with experiment.
