Solitons pp 137-152 | Cite as

The Large-Nc Renormalization Group

  • Nicholas Dorey
  • Michael P. Mattis
Conference paper
Part of the CRM Series in Mathematical Physics book series (CRM)


In this chapter1, 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 l/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 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-Δ 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 Λ → ∞.


Renormalization Group Yukawa Coupling Continuum Limit Nuclear Phys Proportionality Rule 
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© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Nicholas Dorey
  • Michael P. Mattis

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