The large-N-c renormalization group

In this chapter(1), we review how effective theories of mesons and baryons become exactly soluble in the large-N-c limit. We start with a generic hadr on Lagrangian constrained only by certain well-known large-N-c selection ru les. The bare vertices of the theory are dressed by an infinite class of UV divergent Feynman diagrams at leading order in 1/N-c. We show how all thes e leading-order diagrams can be summed exactly using semiclassical techniqu es. The saddle-point field configuration is reminiscent of the chiral bag: hedgehog pions outside a sphere of radius Lambda(-1) (Lambda being the UV c utoff of the effective theory) matched onto nucleon degrees of freedom for r less than or equal to Lambda(-1). The effect of this pion cloud is to ren ormalize the bare nucleon mass, nucleon-Delta hyperfine mass splitting, and Yukawa couplings of the theory. The corresponding large-N-c renormalizatio n group equations for these parameters are presented, and solved explicitly in a series of simple models. We explain under what conditions the Skyrmio n emerges as a UV fixed-point of the RG flow as Lambda --> infinity.