  If the fundamental quarks of QCD are replaced by massless adjoint quarks, the
pattern of the chiral symmetry breaking drastically changes compared to the
standard one. It becomes SU(N_f) -> SO(N_f). While for N_f=2 the chiral
Lagrangian describing the 'pion" dynamics is well-known, this is not the case
at N_f>2. We outline a general strategy for deriving chiral Lagrangians for the
coset spaces M_k=SU(k)/SO(k), and study in detail the case of N_f=k=3. We
obtain two- and four-derivatives terms in the chiral Lagrangian on the coset
space M_3 = SU(3)/SO(3), as well as the Wess-Zumino-Novikov-Witten term, in
terms of an explicit parameterization of the quotient manifold. Then we discuss
stable topological solitons supported by this Lagrangian. Aspects of relevant
topological considerations scattered in the literature are reviewed. The same
analysis applies to SO(N) gauge theories with N_f Weyl flavors in the vector
representation.
