Quivers, tilings, branes and rhombi

2005/11/06 by Amihay Hanany, David Vegh · 10 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Homotopy and Cohomology in Algebraic Topology #hep-th

paper · pdf · doi:10.1088/1126-6708/2007/10/029

published as JHEP0710:029,2007 · 36 pages, 40 figures, JHEP3

arxiv created 2005/11/06 · openalex publication_date 2007/10/05 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/01

Abstract

We describe a simple algorithm that computes the recently discovered brane tilings for a given generic toric singular Calabi-Yau threefold. This therefore gives AdS/CFT dual quiver gauge theories for D3-branes probing the given non-compact manifold. The algorithm solves a longstanding problem by computing superpotentials for these theories directly from the toric diagram of the singularity. We study the parameter space of a-maximization; this study is made possible by identifying the R-charges of bifundamental fields as angles in the brane tiling. We also study Seiberg duality from a new perspective.

Citations

• Brane dimers and quiver gauge theories
• On the fate of tachyonic quivers

Cited by

• Brane tilings and reflexive polygons
• Mass-deformed brane tilings
• Brane tilings and non-commutative geometry
• Higgsing M2-brane theories
• Chiral theories of class S S
• Calabi–Yau Volumes and Reflexive Polytopes
• Surface defects and elliptic quantum groups
• Surface defects as transfer matrices
• An introduction to counting orbifolds
• Superconformal index for large N quiver Chern-Simons theories