Baryon physics in a five-dimensional model of hadrons

In 1973 Gerard ’tHooft proposed, in a seminal article [1], a dual description for QCD. He showed that in the limit of large number of colors (Nc) strongly-interacting gauge theories could be described in terms of a weakly-interacting theory of mesons. It was later recognized [2] that, in this dual description, baryons appeared as solitons made of meson fields, as Skyrme had pointed out long before [3]. These solitonic states were therefore referred as skyrmions. Skyrmions have been widely studied in the literature, with some phenomenological successes [4]. Nevertheless, since the full theory of QCD mesons is not known, these studies have been carried out in truncated low-energy models either incorporating only pions [2, 3] or few resonances [4]. It is unclear whether these approaches capture the physics needed to fully describe the baryons, since the stabilization of the baryon size is very sensitive to resonances around the GeV. In the original Skyrme model with only pions, for instance, the inverse skyrmion size ρ s equals the chiral perturbation theory cut-off ΛχPT ∼ 4πFπ (as it should be, since this is the only scale of the model), rendering baryon physics completely incalculable. Other examples are models with the ρ-meson [5] or the ω-meson [6] which were shown to have a stable skyrmion solution. The inverse size, also in this case, is of order