Conductivity of a Clean One-Dimensional Wire

We study the low-temperature low-frequency conductivity $\sigma$ of an interacting one-dimensional electron system in the presence of a periodic potential. The conductivity is strongly influenced by conservation laws, which, we argue, need to be violated by at least two noncommuting umklapp processes to render $\sigma$ finite. The resulting dynamics of the slow modes is studied within a memory matrix approach, and we find an exponential increase as the temperature is lowered, $\sigma \sim (\Delta n{)}^2{e}^{T_0/\left(\mathrm{NT}\right)}$ close to commensurate filling $M/N$, $\Delta n=n-M/N\ll 1$, and $\sigma \sim e^{(T_0^{\prime }/T{)}^{2/3}}$ elsewhere.