Gauge theories from toric geometry and brane tilings
May, 2005
46 pages
Published in:
- JHEP 01 (2006) 128
e-Print:
- hep-th/0505211 [hep-th]
Report number:
- MIT-CTP-3646,
- CERN-PH-TH-2005-084,
- HUTP-05-A0027
Citations per year
Abstract:
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.- gauge field theory: Yang-Mills
- membrane model
- space-time: anti-de Sitter
- field theory: conformal
- space: torus
- geometry: algebra
- fibre bundle
- gauge field theory: quiver
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