Matrix model superpotentials and ADE singularities

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Abstract

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-Yau with corresponding ADE singularities. Moreover, in the additional Ô, Â, D̂ and Ê 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 co-ordinate charts. To obtain these results we develop an algorithm for blowing down exceptional P1, described in the appendix.

Original languageEnglish (US)
Pages (from-to)353-404
Number of pages52
JournalAdvances in Theoretical and Mathematical Physics
Volume12
Issue number2
DOIs
StatePublished - Apr 2008

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Physics and Astronomy(all)

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