Gauge theories from toric geometry and brane tilings

Author: 

Franco, S
Hanany, A
Martelli, D
Sparks, J
Vegh, D
Wecht, B

Publication Date: 

10 April 2006

Journal: 

Journal of High Energy Physics

Last Updated: 

2020-02-22T07:43:54.097+00:00

Issue: 

1

DOI: 

10.1088/1126-6708/2006/01/128

page: 

3295-3334

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 La,b,a, whose smallest member is the Suspended Pinch Point. © SISSA 2006.

Symplectic id: 

12521

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article