Topics in large-N field theory

The first topic develops a technique for a recursive solution to theories in which the fields take values in the group (S)U(N). The general approach is illustrated in a pedagogical treatment of hermitian matrix quantum mechanics. A coset decomposition of SU(N) is used to rewrite a SU(N) symmetric theory as an SU(N-1) theory interacting with additional fields. The technique is applied to the SU(N) continuum chiral model and to two dimensional lattice QCD. In all three cases, the recursive procedure allows in principle for the extraction of the large-N solution as the fixed point of a renormalization group equation. Calculation difficulties make this approach limited to approximate solutions, however. The second topic covers the properties of solitons in an effective chiral lagrangian. Low energy QCD allows for a description of scattering and decays through the techniques of effective lagrangians. In one such model, there are soliton solutions which become the first term in a semiclassical expansion in the large-N approximation