  In this talk we review how effective theories of mesons and baryons become
exactly soluble in the large-N_c limit. We start with a generic hadron
Lagrangian constrained only by certain well-known large-N_c selection rules.
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 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 \Lambda^{-1} (\Lambda being the UV cutoff of
the effective theory) matched onto nucleon degrees of freedom for r <
\Lambda^{-1}. The effect of this pion cloud is to renormalize the bare nucleon
mass, nucleon-\Delta hyperfine mass splitting, and Yukawa couplings of the
theory. The corresponding large-N_c 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 \Lambda --> \infty.
