  We present a field theory analysis of a model of two SU(2n)-invariant
magnetic chains coupled by a generic interaction preserving time reversal and
inversion symmetry. Contrary to the SU(2)-invariant case the zero-temperature
phase diagram of such two-leg spin ladder does not contain topological phases.
Only generalized Valence Bond Solid phases are stabilized when n>1 with
different wave vectors and ground-state degeneracies. In particular, we find a
phase which is made of a cluster of 2n spins put in an SU(2n) singlet state.
For n=3, this cluster phase is relevant to ytterbium ultracold atoms, with an
emergent SU(6) symmetry, loaded in double well optical lattice.
