Matrix model superpotentials and ADE singularities

Details Matrix model superpotentials and ADE singularities Matrix model superpotentials and ADE singularities

2006-12-16

arxiv.org/abs/hep-th/0612172v2

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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