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We consider a one-dimensional electron system, suitable for the descriptionof the electronic correlations in a metallic carbon nanotube. Renormalizationgroup methods are used to study the low-energy behavior of the unscreenedCoulomb interaction between currents of well-defined chirality. In the limit ofa very large number n of subbands we find a strong renormalization of the Fermivelocity, reminiscent of a similar phenomenon in the graphite sheet. For smalln or sufficiently low energy, the Luttinger liquid behavior takes over, with astrong wavefunction renormalization leading to a vanishing quasiparticleweight. Our approach is appropriate to study the crossover from two-dimensionalto one-dimensional behavior in carbon nanotubes of large radius.Comment: 8 pages, 2 figures, LaTeX, PACS: 71.27.+a, 73.20.D, 05.30.F

On the Coulomb interaction in chiral-invariant one-dimensional electron systems