The Hopf Skyrmion in QCD with Adjoint Quarks

Abstract

We consider a modification of QCD in which conventional fundamental quarks are replaced by Weyl fermions in the adjoint representation of the color SU(N). In the case of two flavors the low-energy chiral Lagrangian is that of the Skyrme-Faddeev model. The latter supports topologically stable solitons with mass scaling as N^2. Topological stability is due to the existence of a nontrivial Hopf invariant in the Skyrme-Faddeev model. Our task is to identify, at the level of the fundamental theory, adjoint QCD, an underlying reason responsible for the stability of the corresponding hadrons. We argue that all "normal" mesons and baryons, with mass O(N^0), are characterized by (-1)^Q (-1)^F =1, where Q is a conserved charge corresponding to the unbroken U(1) surviving in the process of the chiral symmetry breaking (SU(2) \to U(1) for two adjoint flavors). Moreover, F is the fermion number (defined mod 2 in the case at hand). We argue that there exist exotic hadrons with mass O(N^2) and (-1)^Q (-1)^F = -1. They are in one-to-one correspondence with the Hopf Skyrmions. The transition from nonexotic to exotic hadrons is due to a shift in F, namely F \to F - {\cal H} where {\cal H} is the Hopf invariant. To detect this phenomenon we have to extend the Skyrme-Faddeev model by introducing fermions.

18 pages, 3 figures; v.2: a reference and a comment added; v.3: two comments added, figures improved

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• Gluequark Dark Matter
• Remarks on Adjoint QCD with k Flavors, k>= 2
• Spin contribution to light baryons in different large-$N$ limits
• Revisiting the Faddeev-Skyrme Model and Hopf Solitons
• Skyrmions in Yang--Mills Theories with Massless Adjoint Quarks
• Baryon resonances in large $N_c$ QCD
• Low-Energy Limit of Yang-Mills with Massless Adjoint Quarks: Chiral Lagrangian and Skyrmions
• Supersymmetric Q Solitons of Arbitrary Genus
• Skyrmions in Orientifold and Adjoint QCD
• Experimental and Theoretical Evidence for Extended Particle Models
• Deformation of the CP(1) model leading to fixed size solitons in 2+1 dimensions