  Recently, Haldane's conjecture about SU(2) chains has been generalized to
SU($n$) chains in the symmetric representations. For a rank-$p$ representation,
a gapless phase is predicted when $p$ and $n$ are coprime; otherwise, a finite
energy gap is present above the ground state. In this work, we offer an
intuitive explanation of this behavior based on fractional topological
excitations, which are able to generate a mass gap except when $p$ and $n$ have
no common divisor. This is a generalization of an older work in SU(2), which
explains the generation of the Haldane gap in terms of merons in the O(3)
nonlinear sigma model.
