Brane Tilings and Non-Commutative Geometry
High Energy Physics - Theory
2011-03-18 v2 Algebraic Geometry
Abstract
We derive the quiver gauge theory on the world-volume of D3-branes transverse to an L(a,b,c) singularity by computing the endomorphism algebra of a tilting object first constructed by Van den Bergh. The quiver gauge theory can be concisely specified by an embedding of a graph into a face-centered cubic lattice. In this description, planar Seiberg dualities of the gauge theory act by changing the graph embedding. We use this description of Seiberg duality to show these quiver gauge theories possess periodic Seiberg dualities whose existence was expected from the AdS/CFT correspondence.
Cite
@article{arxiv.1003.2862,
title = {Brane Tilings and Non-Commutative Geometry},
author = {Richard Eager},
journal= {arXiv preprint arXiv:1003.2862},
year = {2011}
}
Comments
23 pages; v2: reference added, minor changes