  We derive and analyze the low-energy theory of superconductivity in carbon
nanotube ropes. A rope is modelled as an array of metallic nanotubes, taking
into account phonon-mediated as well as Coulomb interactions, and arbitrary
Cooper pair hopping amplitudes (Josephson couplings) between different tubes.
We use a systematic cumulant expansion to construct the Ginzburg-Landau action
including quantum fluctuations. The regime of validity is carefully
established, and the effect of phase slips is assessed. Quantum phase slips are
shown to cause a depression of the critical temperature $T_c$ below the
mean-field value, and a temperature-dependent resistance below $T_c$. We
compare our theoretical results to recent experimental data of Kasumov {\sl et
al.} [Phys. Rev. B {\bf 68}, 214521 (2003)] for the sub-$T_c$ resistance, and
find good agreement with only one free fit parameter. Ropes of nanotubes
therefore represent superconductors in the one-dimensional few-channel limit.
