Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-12-19
J.Phys.A40:6221-6238,2007
Physics
High Energy Physics
High Energy Physics - Theory
23 pages, 2 figures; v.2 references added, a comment added; final version to be published in J. Phys. A
Scientific paper
10.1088/1751-8113/40/23/015
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.
Auzzi Roberto
Shifman Michael
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