Gauge Theories from Toric Geometry and Brane Tilings

Details Gauge Theories from Toric Geometry and Brane Tilings Gauge Theories from Toric Geometry and Brane Tilings

2005-05-24

arxiv.org/abs/hep-th/0505211v3

JHEP 0601 (2006) 128

Physics

High Energy Physics

High Energy Physics - Theory

46 pages, 21 figures, JHEP3. v2: minor changes and references added. v3: typos and two figures corrected

Scientific paper

10.1088/1126-6708/2006/01/128

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 L^{a,b,a}, whose smallest member is the Suspended Pinch Point.

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