Gauge theories from toric geometry and brane tilings

Franco, Sebastian; Hanany, Amihay; Martelli, Dario; Sparks, James; Vegh, David; Wecht, Brian

doi:10.1088/1126-6708/2006/01/128

Gauge theories from toric geometry and brane tilings

Franco, Sebastian; Hanany, Amihay; Martelli, Dario; Sparks, James; Vegh, David; Wecht, Brian

Authors

Sebastian Franco

Amihay Hanany

Dario Martelli

James Sparks

David Vegh

Brian Wecht

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 La,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.

Citation

Franco, S., Hanany, A., Martelli, D., Sparks, J., Vegh, D., & Wecht, B. (2006). Gauge theories from toric geometry and brane tilings. Journal of High Energy Physics, 2006(01), Article 128. https://doi.org/10.1088/1126-6708/2006/01/128

Journal Article Type	Article
Publication Date	Jan 20, 2006
Deposit Date	Jan 27, 2014
Publicly Available Date	Feb 14, 2014
Journal	Journal of High Energy Physics
Print ISSN	1126-6708
Electronic ISSN	1029-8479
Publisher	Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed	Peer Reviewed
Volume	2006
Issue	01
Article Number	128
DOI	https://doi.org/10.1088/1126-6708/2006/01/128
Keywords	AdS-CFT and dS-CFT Correspondence, D-branes.