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 be violated by at least two non-commuting Umklapp processes to render sigma finite. The resulting dynamics of the slow modes is studied within a memory matrix approach, and we find exponential increase as the temperature is lowered, sigma = (Delta n)^2 e^{T_0/(N T)} close to commensurate filling M/N, Delta n=n-M/N << 1, and sigma = e^{(T’_0/T)^{2/3}} elsewhere.