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

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.

arXiv comment23 pages, 2 figures; v.2 references added, a comment added; final version to be published in J. Phys. A

References in corpus (18)

• Knots and Particles
• The spectrum of the QCD Dirac operator and chiral random matrix theory: the threefold way
• Exact Results in Non-Supersymmetric Large N Orientifold Field Theories
• Solitons, Links and Knots
• Spectral sum rules and finite volume partition function in gauge theories with real and pseudoreal fermions
• Effective Lagrangians and Chiral Random Matrix Theory
• Instantons in Partially Broken Gauge Groups
• Baryons and Skyrmions in QCD with Quarks in Higher Representations
• The Hopf Skyrmion in QCD with Adjoint Quarks
• Fermionic quantization of Hopf solitons
• Presentations of the first homotopy groups of the unitary groups
• Toroidal Confugurations As Stable Solitons
• From Super-Yang-Mills Theory to QCD: Planar Equivalence and its Implications
• QCD Flux Tubes as Sigma Model Relics
• Confining Flux Tubes in a Current Algebra Approach
• Semiclassical Quantization of Hopf Solitons
• Homogeneous spaces and Faddeev-Skyrme models
• Central Extensions of Gauge Groups Revisited

Cited by in corpus (8)

• Orbifold equivalence and the sign problem at finite baryon density
• The Hopf Skyrmion in QCD with Adjoint Quarks
• Fermionic Hopf solitons and Berry's phase in topological surface superconductors
• Non-Abelian Alice strings in two-flavor dense QCD
• Skyrmions in Yang--Mills Theories with Massless Adjoint Quarks
• Topological confinement of vortices in two-flavor dense QCD
• Skyrmions in Orientifold and Adjoint QCD
• Topological physics in the standard model and beyond