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

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

1993-06-03

arxiv.org/abs/hep-th/9306018v1

Nucl.Phys. B408 (1993) 600-634

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1016/0550-3213(93)90382-Y

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.

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