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Matrix model superpotentials and Cal...

Curto, Carina.

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Matrix model superpotentials and Calabi-Yau spaces: An A-D-E classification.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Matrix model superpotentials and Calabi-Yau spaces: An A-D-E classification./
作者:	Curto, Carina.
面頁冊數:	177 p.
附註:	Source: Dissertation Abstracts International, Volume: 66-09, Section: B, page: 4843.
Contained By:	Dissertation Abstracts International66-09B.
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoeng/servlet/advanced?query=3187950
ISBN:	9780542303470

Matrix model superpotentials and Calabi-Yau spaces: An A-D-E classification.
Curto, Carina.

Matrix model superpotentials and Calabi-Yau spaces: An A-D-E classification. - 177 p.

Source: Dissertation Abstracts International, Volume: 66-09, Section: B, page: 4843.

Thesis (Ph.D.)--Duke University, 2005.

We use F. Ferrari's methods relating matrix models to Calabi-Yau spaces in order to explain Intriligator and Wecht's ADE classification of N = 1 superconformal theories which arise as RG fixed points of N = 1 SQCD theories with adjoints. The connection between matrix models and N = 1 gauge theories can be seen as evidence for the Dijkgraaf-Vafa conjecture. We find that ADE superpotentials in the Intriligator-Wecht classification exactly match matrix model superpotentials obtained from Calabi-Yau's with corresponding ADE singularities. Moreover, in the additional O, A, D&circ; 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 coordinate charts. To obtain these results we develop techniques for performing small resolutions and small blow-downs, including an algorithm for blowing down exceptional P1 's. In particular, we conjecture that small resolutions for isolated Gorenstein threefold singularities can be obtained by deforming matrix factorizations for simple surface singularities - and prove this in the length 1 and length 2 cases.

ISBN: 9780542303470Subjects--Topical Terms:

515831
Mathematics.

Matrix model superpotentials and Calabi-Yau spaces: An A-D-E classification.
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502 $a Thesis (Ph.D.)--Duke University, 2005.
520 $a We use F. Ferrari's methods relating matrix models to Calabi-Yau spaces in order to explain Intriligator and Wecht's ADE classification of N = 1 superconformal theories which arise as RG fixed points of N = 1 SQCD theories with adjoints. The connection between matrix models and N = 1 gauge theories can be seen as evidence for the Dijkgraaf-Vafa conjecture. We find that ADE superpotentials in the Intriligator-Wecht classification exactly match matrix model superpotentials obtained from Calabi-Yau's with corresponding ADE singularities. Moreover, in the additional O, A, D&circ; 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 coordinate charts. To obtain these results we develop techniques for performing small resolutions and small blow-downs, including an algorithm for blowing down exceptional P1 's. In particular, we conjecture that small resolutions for isolated Gorenstein threefold singularities can be obtained by deforming matrix factorizations for simple surface singularities - and prove this in the length 1 and length 2 cases.
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