Conductivity of a Luttinger liquid

We show that the real part of the frequency-dependent conductivity of interacting spinless fermions at incommensurate band fillings in one dimension at T=0 is proportional to ${\mathrm{\omega }}^3$ for small positive frequencies, contrary to statements in the recent literature. We argue that the dc conductivity of spinless fermions at incommensurate band fillings diverges faster than any power of 1/T as T→0. We give the extension of our results to the case of commensurate band fillings and fermions with spin.