  Building on the generalization of the exactly dimerized Majumdar-Ghosh ground
state to arbitrary spin S for the Heisenberg chain with a three-site term
(S_{i-1} S_i)(S_i S_{i+1}) + H.c., we use density-matrix renormalization group
simulations and exact diagonalizations to determine the nature of the
dimerization transition for S=1, 3/2 and 2. The resulting central charge and
critical exponent are in good agreement with the SU(2)_{k=2S}
Wess-Zumino-Witten values c=3k/(2+k) and \eta=3/(2+k). Since the 3-site term
that induces dimerization appears naturally if exchange interactions are
calculated beyond second order, these results suggest that SU(2)_{k>1}
Wess-Zumino-Witten models might finally be realized in actual spin chains.
