Three-Dimensional Gorenstein Singularities and SU(3) Modular Invariants
Jun S. Song
Abstract
Using N=2 Landau-Ginzburg theories, we examine the recent conjectures relating the SU(3) WZW modular invariants, finite subgroups of SU(3) and Gorenstein singularities. All isolated three-dimensional Gorenstein singularities do not appear to be related to any known Landau-Ginzburg theories, but we present some curious observations which suggest that the SU(3)n/SU(2)xU(1) Kazama-Suzuki model may be related to a deformed geometry of C3/Zn+3xZn+3. The toric resolution diagrams of those particular singularities are also seen to be classifying the diagonal modular invariants of the SU(3)n as well as the SU(2)n+1 WZW models.
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