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June 2008 Dimer Models from Mirror Symmetry and Quivering Amoebae
Bo Feng, Yang-Hui He, Kristian D. Kennaway, Cumrun Vafa
Adv. Theor. Math. Phys. 12(3): 489-545 (June 2008).

Abstract

Dimer models are 2-dimensional combinatorial systems that have been shown to encode the gauge groups, matter content and tree-level superpotential of the world-volume quiver gauge theories obtained by placing D3-branes at the tip of a singular toric Calabi–Yau cone. In particular the dimer graph is dual to the quiver graph. However, the string theoretic explanation of this was unclear. In this paper we use mirror symmetry to shed light on this: the dimer models live on a T2 subspace of the T3 fibre that is involved in mirror symmetry and is wrapped by D6-branes. These D6-branes are mirror to the D3-branes at the singular point, and geometrically encode the same quiver theory on their world-volume.

Citation

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Bo Feng. Yang-Hui He. Kristian D. Kennaway. Cumrun Vafa. "Dimer Models from Mirror Symmetry and Quivering Amoebae." Adv. Theor. Math. Phys. 12 (3) 489 - 545, June 2008.

Information

Published: June 2008
First available in Project Euclid: 7 May 2008

zbMATH: 1144.81501
MathSciNet: MR2399318

Rights: Copyright © 2008 International Press of Boston

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Vol.12 • No. 3 • June 2008
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