Abstract
The discovery of integrable N = 2 supersymmetric Landau-Ginzburg theories whose chiral rings are fusion rings suggests a close connection between 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 superpotentials with Sp( N) K and SU( N) K fusion rings as chiral rings. The chiral rings of the new superpotentials are not directly the fusion rings of any conformal field theory, although they are natural quotients of the tensor subring of the SO( N) K fusion ring. The new superpotentials yield solvable (twisted N = 2) topological field theories. We obtain the integer-valued correlation functions as sums of SO( N) K Verlinde dimensions by expressing the correlators as fusion residues. The SO(2 n + 1) 2 k + 1 and SO(2 k + 1) 2 n + 1 related topological Landau-Ginzburg theories are isomorphic, despite being defined via quite different superpotentials.
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