University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Faculty Publications, Department of Mathematics Mathematics, Department of 2008 Matrix model superpotentials and ADE singularities Carina Curto University of Nebraska - Lincoln,
[email protected] Follow this and additional works at: https://digitalcommons.unl.edu/mathfacpub Part of the Mathematics Commons Curto, Carina, "Matrix model superpotentials and ADE singularities" (2008). Faculty Publications, Department of Mathematics. 34. https://digitalcommons.unl.edu/mathfacpub/34 This Article is brought to you for free and open access by the Mathematics, Department of at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Faculty Publications, Department of Mathematics by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. c 2008 International Press Adv. Theor. Math. Phys. 12 (2008) 355–406 Matrix model superpotentials and ADE singularities Carina Curto Department of Mathematics, Duke University, Durham, NC, USA CMBN, Rutgers University, Newark, NJ, USA
[email protected] 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 classifi- cation of N = 1 superconformal theories which arise as RG fixed points of N = 1 SQCD theories with adjoints. We find that ADE superpoten- tials in the Intriligator–Wecht classification exactly match matrix model superpotentials obtained from Calabi–Yau with corresponding ADE sin- gularities. Moreover, in the additional O, A, D and 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 co-ordinate charts.