  Dynamics of SU(N_c) Yang--Mills theories with N_f adjoint Weyl fermions is
quite different from that of SU(N_c) gauge theories with fundamental quarks.
The symmetry breaking pattern is SU(N_f) --> SO(N_f). The corresponding sigma
model supports Skyrmions whose microscopic identification is not immediately
clear. We address this issue as well as the issue of the Skyrmion stability.
The case of N_f=2 had been considered previously. Here we discuss N_f >= 3. We
discuss the coupling between the massless Goldstone bosons and massive
composite fermions (with mass O(N_c^0)) from the standpoint of the low-energy
chiral sigma model. We derive the Wess--Zumino--Novikov--Witten term and then
determine Skyrmion statistics. We also determine their fermion number (mod 2)
and observe an abnormal relation between the statistics and the fermion number.
This explains the Skyrmion stability. In addition, we consider another
microscopic theory -- SO(N_c) Yang--Mills with N_f Weyl fermions in the
vectorial representation -- which has the same chiral symmetry breaking pattern
and the same chiral Lagrangian. We discuss distinctive features of these two
scenarios.
