ar X iv : h ep - p h / 95 04 32 8 v 1 1 8 A pr 1 99 5 The Large - N c Renormalization Group

In this talk1, we review how effective theories of mesons and baryons become exactly soluble in the large-Nc limit. We start with a generic hadron Lagrangian constrained only by certain well-known large-Nc selection rules. The bare vertices of the theory are dressed by an infinite class of UV divergent Feynman diagrams at leading order in 1/Nc. We show how all these leading-order diagrams can be summed exactly using semiclassical techniques. The saddle-point field configuration is reminiscent of the chiral bag: hedgehog pions outside a sphere of radius Λ−1 (Λ being the UV cutoff of the effective theory) matched onto nucleon degrees of freedom for r ≤ Λ−1. The effect of this pion cloud is to renormalize the bare nucleon mass, nucleon-∆ hyperfine mass splitting, and Yukawa couplings of the theory. The corresponding large-Nc renormalization group equations for these parameters are presented, and solved explicitly in a series of simple models. We explain under what conditions the Skyrmion emerges as a UV fixed-point of the RG flow as Λ → ∞. Introduction. The large-Nc limit of QCD [1] is thought to retain all the important dynamical features of the realistic case, such as confinement, chiral symmetry breaking and asymptotic freedom, while at the same time offering considerable simplifications for the effective theory of hadrons. The effective theory of mesons becomes semiclassical in this limit and Witten [2] has argued that large-Nc baryons should be identified with chiral soliton solutions of the corresponding meson field equations. Talk presented at the 1995 International Workshop on Nuclear and Particle Physics in Seoul, Korea