Low-Energy Limit of Yang-Mills with Massless Adjoint Quarks: Chiral Lagrangian and Skyrmions

TL;DR

This paper explores the low-energy behavior of Yang-Mills theories with massless adjoint quarks, deriving chiral Lagrangians for specific symmetry breaking patterns and analyzing topological solitons in these models.

Contribution

It provides a systematic method for deriving chiral Lagrangians for SU(k)/SO(k) coset spaces and applies it to the case N_f=k=3, including the Wess-Zumino-Novikov-Witten term and soliton analysis.

Findings

Derived explicit two- and four-derivative chiral Lagrangian terms for SU(3)/SO(3).

Included the Wess-Zumino-Novikov-Witten term in the Lagrangian.

Analyzed stable topological solitons supported by the Lagrangian.

Abstract

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.