Conductivity in Pseudogapped Superconductors: The Role of the Fermi Arcs

We calculate the dc conductivity $\sigma$ in a pseudogapped high $T_c$ superconductor within a theory which is consistent with gauge invariance. Our results contain additional terms beyond those identified previously. Although it has been thought that lifetime effects dominate the $T$ dependence of transport, here we show (consistent with growing experimental support) that the temperature dependence of the effective carrier number $(n\mathrm{/}m(T){)}_{\mathrm{e}\mathrm{f}\mathrm{f}}$ plays a critical role and thereby leads to the contrasting behavior between over and under-doped regimes. The role of Fermi arcs is secondary.