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We study a system of two Tomonaga-Luttinger models coupled by a smalltransverse hopping (a two-chain ladder). We use Abelian and non-Abelianbosonisation to show that the strong coupling regime at low energies can bedescribed by an SO(5)$_1$ WZW model (or equivalently 5 massless Majoranafermions) deformed by symmetry breaking terms that nonetheless leave the theorycritical at T=0. The SO(5) currents of the theory comprise the charge and spincurrents and linear combinations of the so-called pi operators (S.C. Zhang,Science 275, 1089 (1997)) which are local in terms both of the originalfermions and those of the effective theory. Using bosonisation we obtain theasymptotic behaviour of all correlation functions. We find that the 5 component``superspin'' vector has power law correlations at T=0; other fermion bilinearshave exponentially decaying correlations and the corresponding tendencies aresuppressed. Conformal field theory also allows us to obtain the energies,quantum numbers, and degeneracies of the low-lying states and fit them intodeformed SO(5) multiplets.Comment: 17 pages, ReVTeX, 1 eps figure include

SO(5)-symmetric description of the low-energy sector of a ladder system