Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-12-16
Advances in Theoretical and Mathematical Physics, Volume 12, Issue 2. (2008)
Physics
High Energy Physics
High Energy Physics - Theory
52 pages. Last line of abstract and two references added; no other changes from previous version
Scientific paper
We use F. Ferrari's methods relating matrix models to Calabi-Yau spaces in order to explain much of Intriligator and Wecht's ADE classification of $\N=1$ superconformal theories which arise as RG fixed points of $\N = 1$ SQCD theories with adjoints. We find that ADE superpotentials in the Intriligator-Wecht classification exactly match matrix model superpotentials obtained from Calabi-Yaus with corresponding ADE singularities. Moreover, in the additional $\Hat{O}, \Hat{A}, \Hat{D}$ and $\Hat{E}$ cases we find new singular geometries. These `hat' geometries are closely related to their ADE counterparts, but feature non-isolated singularities. As a byproduct, we give simple descriptions for small resolutions of Gorenstein threefold singularities in terms of transition functions between just two coordinate charts. To obtain these results, we develop an algorithm for blowing down exceptional $\PP^1$s, described in the appendix.
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