Skyrmions and effective Lagrangians

The need to model quantum chromodynamics (QCD) at low energy is emphasized. An outline of the1/NC expansion of QCD, for large NC, shows the deep link between the Skyrme effective Lagrangian and QCD. The Skyrme model, built from the nonlinear σ model plus a stabilizer term related to vector dominance, is briefly described. The model satisfies like QCD chiral symmetry. We illustrate how the gauged Wess–Zumino action demonstrates that the topological current can be identified with the baryon current. We recall how one can show that the topological soliton is a fermion for odd NC. An example of an effective Lagrangian, built from π and low-mass vector mesons, ω, ρ, and A1 fields, is given. It describes rather well low-energy meson and baryon physics. Predictions of effective Lagrangians of the Skyrme type on meson–meson, meson–baryon, and baryon–baryon scatterings at low energy are depicted. A two-phase chiral symmetric model, the chiral bag, is introduced. It contains an inner core of confined quarks and gluons surrounded by meson fields in the topological configuration of a Skyrmion. It can describe nuclei from the low- to the high-energy range.