Correlation effects in carbon nanotubes

We consider the effects of Coulomb interactions on single-wall carbon nanotubes using an on-site Hubbard interaction, u. For the (N,N) armchair tubes the low-energy theory is shown to be identical to a two-chain Hubbard model at half-filling, with an effective interaction u_N=u/N. Umklapp scattering leads to gaps in the spectrum of charge and spin excitations which are exponentially small for large N. Above the gaps the intrinsic nanotube resistivity due to these scattering processes is linear in temperature, as observed experimentally. The presence of ``d-wave'' superconductivity in the two-chain Hubbard model away from half-filling suggests that doped armchair nanotubes might exhibit superconductivity with a purely electronic mechanism.