From Effective Lagrangians, to Chiral Bags, to Skyrmions with the Large-N_c Renormalization Group

Abstract

We explicitly relate effective meson-baryon Lagrangian models, chiral bags, and Skyrmions in the following way. First, effective Lagrangians are constructed in a manner consistent with an underlying large-N_c QCD. An infinite set of graphs dress the bare Yukawa couplings at *leading* order in 1/N_c, and are summed using semiclassical techniques. What emerges is a picture of the large-N_c baryon reminiscent of the chiral bag: hedgehog pions for r > 1/\Lambda patched onto bare nucleon degrees of freedom for r < 1/\Lambda, where the ``bag radius'' 1/\Lambda is the UV cutoff on the graphs. Next, a novel renormalization group (RG) is derived, in which the bare Yukawa couplings, baryon masses and hyperfine baryon mass splittings run with \Lambda. Finally, this RG flow is shown to act as a *filter* on the renormalized Lagrangian parameters: when they are fine-tuned to obey Skyrme-model relations the continuum limit \Lambda --> \infty exists and is, in fact, a Skyrme model; otherwise there is no continuum limit.