  We revisit correlation effects in doped metallic zigzag carbon nanotubes by
using both the one-loop renormalization group and non-perturbative bosonization
techniques. Note that, if a nanotube is placed near a conducting plate, the
long-range Coulomb interactions are screened and the resulting short-range
interactions can be modelled by on-site and nearest-neighbor repulsive
interactions $U$, $V$ and $V_{\perp}$ respectively. Using both analytic and
numeric means, we determine the phase diagram of the ground states. For
$U/t<0.5$ ($t$ is the hopping strength), dynamical symmetry enlargement occurs
and the low-energy excitations are described by the SO(6) Gross-Neveu model.
However, for realistic material parameters $U/t \sim \mathcal{O}(1)$, the
charge sector decouples but there remains an enlarged SO(4) symmetry in the
spin sector.
