  We present a low-energy effective field theory to describe the SO(n)
bilinear-biquadratic spin chain. We start with n=6 and construct the effective
theory by using six Majorana fermions. After determining various correlation
functions we characterize the phases and establish the relation between the
effective theories for SO(6) and SO(5). Together with the known results for n=3
and 4, a reduction mechanism is proposed to understand the ground state for
arbitrary SO(n). Also, we provide a generalization of the Lieb-Schultz-Mattis
theorem for SO(n). The implications of our results for entanglement and
correlation functions are discussed.
