Gauge theories from toric geometry and brane tilings

May, 2005
46 pages
Published in:
  • JHEP 01 (2006) 128
e-Print:
Report number:
  • MIT-CTP-3646,
  • CERN-PH-TH-2005-084,
  • HUTP-05-A0027

Citations per year

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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