INTEGRABLE N=2 LANDAU-GINZBURG THEORIES FROM QUOTIENTS OF FUSION RINGS

The discovery of integrable N = 2 supersymmetric Landau-Ginzburg theor ies whose chiral rings are fusion rings suggests a close connection be tween fusion rings, the related Landau-Ginzburg superpotentials, and N = 2 quantum integrability. We examine this connection by finding the natural SO(N)K analogue of the construction that produced the superpot entials with Sp(N)K and SU(N)K fusion rings as chiral rings. The chira l rings of the new superpotentials are not directly the fusion rings o f any conformal field theory, although they are natural quotients of t he tensor subring of the SO(N)K fusion ring. The new superpotentials y ield solvable (twisted N = 2) topological field theories. We obtain th e integer-valued correlation functions as sums of SO(N)K Verlinde dime nsions by expressing the correlators as fusion residues. The SO(2n + 1 )2k + 1 and SO(2k + 1)2n + 1 related topological Landau-Ginzburg theor ies are isomorphic, despite being defined via quite different superpot entials.