  We study a system of two Tomonaga-Luttinger models coupled by a small
transverse hopping (a two-chain ladder). We use Abelian and non-Abelian
bosonisation to show that the strong coupling regime at low energies can be
described by an SO(5)$_1$ WZW model (or equivalently 5 massless Majorana
fermions) deformed by symmetry breaking terms that nonetheless leave the theory
critical at T=0. The SO(5) currents of the theory comprise the charge and spin
currents and linear combinations of the so-called pi operators (S.C. Zhang,
Science 275, 1089 (1997)) which are local in terms both of the original
fermions and those of the effective theory. Using bosonisation we obtain the
asymptotic behaviour of all correlation functions. We find that the 5 component
``superspin'' vector has power law correlations at T=0; other fermion bilinears
have exponentially decaying correlations and the corresponding tendencies are
suppressed. Conformal field theory also allows us to obtain the energies,
quantum numbers, and degeneracies of the low-lying states and fit them into
deformed SO(5) multiplets.
