TY - JOUR

T1 - Low-energy limit of Yang-Mills with massless adjoint quarks

T2 - Chiral Lagrangian and Skyrmions

AU - Auzzi, R.

AU - Shifman, M.

PY - 2007/6/8

Y1 - 2007/6/8

N2 - 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.

AB - 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.

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U2 - 10.1088/1751-8113/40/23/015

DO - 10.1088/1751-8113/40/23/015

M3 - Article

AN - SCOPUS:34249684405

SN - 1751-8113

VL - 40

SP - 6221

EP - 6237

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 23

M1 - 015

ER -