Methods in non-perturbative field theory

The authors discuss some examples of quantum field theories which are either exactly solved or greatly simplified in N=∞ limit. 1/N expansion appears at present to be the most promising tool to investigate non-perturbative phenomena in field theory. In particular in the case of theories where dimensional transmutation is expected to take place 1/N is the only expansion parameter of the theory (coupling constant g is traded for the mass gap as in (11) and is not an expansion parameter ) and the theory will never be solved unless it is solved in N=∞ limit. In the last year another made an observation that baryons in N=∞ QCD are realized as solitons in chiral Lagrangian which incorporates the structure of the anomaly of underlying gauge theory. This result seems to indicate that there exists a possibility of unifying various approaches to strong interaction physics proposed in the past, chiral dynamics, dual theory, strong coupling theory etc. within the framework of 1/N expansion. Analytic solution of N=∞ gauge field will undoubtedly give us a wealth of information on strong interaction dynamics. Unfortunately, the authors are very far from achieving this goal