Graph Rings and Integrable Perturbations of $N=2$ Superconformal Theories

Abstract

We show that the connection between certain integrable perturbations of $N=2$ superconformal theories and graphs found by Lerche and Warner extends to a broader class. These perturbations are such that the generators of the perturbed chiral ring may be diagonalized in an orthonormal basis. This allows to define a dual ring, whose generators are labelled by the ground states of the theory and are encoded in a graph or set of graphs, that reproduce the pattern of the ground states and interpolating solitons. All known perturbations of the $ADE$ potentials and some others are shown to satisfy this criterion. This suggests a test of integrability.

44 pages, uuencoded, compressed tar file using harvmac and epsf, four figures included, Saclay preprint SPhT 93/057

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• Elliptic Genera and the Landau-Ginzburg Approach to N=2 Orbifolds
• Comments on D-branes in Kazama-Suzuki models and Landau-Ginzburg theories
• Frobenius manifolds associated to Coxeter groups of type E_7 and E_8