TL;DR
This paper constructs quiver gauge theories for D3-branes at specific singularities using non-commutative geometry, revealing periodic Seiberg dualities consistent with AdS/CFT predictions.
Contribution
It introduces a novel geometric representation of quiver gauge theories via face-centered cubic lattice embeddings, linking Seiberg duality to graph transformations.
Findings
Quiver gauge theories are specified by lattice-embedded graphs.
Planar Seiberg dualities correspond to graph embedding changes.
Existence of periodic Seiberg dualities confirmed.
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.
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