  Skyrmions are present in many models of electroweak symmetry breaking where
the Higgs is a pseudo-Goldstone boson of some strongly interacting sector. They
are stable, composite objects whose mass lies in the range 10-100 TeV and can
be naturally abundant in the universe due to their small annihilation
cross-section. They represent therefore good dark matter candidates. We show
however in this work that the lightest skyrmion states are electrically charged
in most of the popular little Higgs models, and hence should have been directly
or indirectly observed in nature already. The charge of the skyrmion under the
electroweak gauge group is computed in a model-independent way and is related
to the presence of anomalies in the underlying theory via the
Wess-Zumino-Witten term.
