  We investigate theoretically an interacting metallic wire with a strong
magnetic field directed along its length and show that it is a new and highly
tunable one-dimensional system. By considering a suitable change in spatial
geometry, we map the problem in the zeroth Landau level with Landau level
degeneracy $N$ to one-dimensional fermions with an $N$-component pseudospin
degree of freedom and $SU(2)$-symmetric interactions. This mapping allows us to
establish the phase diagram as a function of the interactions for small $N$
(and make conjectures for large $N$) using renormalization group and
bosonization techniques. We find pseudospin-charge separation with a gapless
$U(1)$ charge sector and several possible strong-coupling phases in the
pseudospin sector. For odd $N$, we find a fluctuating pseudospin-singlet charge
density wave phase and a fluctuating pseudospin-singlet superconducting phase
which are topologically distinct. For even $N>2$, similar phases exist,
although they are not topologically distinct, and an additional, novel
pseudospin-gapless phase appears. We discuss experimental conditions for
observing our proposals.
