Skyrmions in Yang-Mills theories with massless adjoint quarks

Dynamics of SU(Nc) Yang-Mills theories with Nf adjoint Weyl fermions is quite different from that of SU(Nc) gauge theories with fundamental quarks. The symmetry breaking pattern is SU(Nf)→SO(Nf). 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 Nf=2 had been considered previously. Here we discuss Nf≥3. We discuss the coupling between the massless Goldstone bosons and massive composite fermions [with mass O(Nc0)] 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 (mod2) 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(Nc) Yang-Mills with Nf 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.