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(Nf) → SO(Nf). While for Nf ≤ 2, the chiral Lagrangian describing the 'pion' dynamics is well known, this is not the case at Nf > 2. We outline a general strategy for deriving chiral Lagrangians for the coset spaces and study in detail the case of Nf ≤ k ≤ 3. We obtain two- and four-derivatives terms in the chiral Lagrangian on the coset space ≤ 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 Nf Weyl flavours in the vector representation.
|Original language||English (US)|
|Number of pages||17|
|Journal||Journal of Physics A: Mathematical and Theoretical|
|State||Published - Jun 8 2007|