Affine Algebras and Strong Interaction Theories

Abstract

A new infinite parameter symmetry, the Kac-Moody Lie algebras, appears in several different connections with theories of the strong Interactions. Its explicit representation in terms of the dual string is reviewed here in simple language. A nonlocal nonlinear realization of a subalgebra of the affine algebras on the self-dual class of solutions of the Yang Mills theory is also reviewed. It is remarked that this structure occurs naturally in a Kaluza-Klein search for the new symmetry on the full gauge theory. The existence of the same invariance in these different models of the hadrons may serve to unify the descriptions and lead to solvability in the nonperturbative regime.