Gauge theories from toric geometry and brane tilings

Journal article

We provide a general set of rules for extracting the data defining a quiver gauge theory from a given toric Calabi-Yau singularity. Our method combines information from the geometry and topology of Sasaki-Einstein manifolds, AdS/CFT, dimers, and brane tilings. We explain how the field content, quantum numbers, and superpotential of a superconformal gauge theory on D3-branes probing a toric Calabi-Yau singularity can be deduced. The infinite family of toric singularities with known horizon Sasaki-Einstein manifolds L a,b,c is used to illustrate these ideas. We construct the corresponding quiver gauge theories, which may be fully specified by giving a tiling of the plane by hexagons with certain gluing rules. As checks of this construction, we perform a-maximisation as well as Z-minimisation to compute the exact R-charges of an arbitrary such quiver. We also examine a number of examples in detail, including the infinite subfamily La,b,a, whose smallest member is the Suspended Pinch Point. © SISSA 2006.

Authors: Franco, S; Hanany, A; Martelli, D; Sparks, J; Vegh, D

• Publication status: Published
• Journal: JOURNAL OF HIGH ENERGY PHYSICS
• Volume: 2006
• Issue: 1
• Pages: 3295-3334
• Publication date: 2006-01-01
• DOI: 10.1088/1126-6708/2006/01/128
• EISSN: 1029-8479
• ISSN: 1029-8479
• Language: English
• Keywords: D-branes; AdS-CFT correspondence