2003/10/31 by Christopher P. Herzog, Christopher P Herzog · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Conformal map #Gauge (firearms) #Gauge theory #Homotopy and Cohomology in Algebraic Topology #Permutation (music) #Quiver #Simple (philosophy) #Supersymmetric gauge theory #hep-th
paper · pdf · doi:10.1088/1126-6708/2004/04/069
published as JHEP 0404 (2004) 069 · 26 pages, 1 figure; v2 footnote 2 amended; v3 ref added
arxiv created 2004/02/16 · openalex publication_date 2004/04/30 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
Stacks of D3-branes placed at the tip of a cone over a del Pezzo surface provide a way of geometrically engineering a small but rich class of gauge/gravity dualities. We develop tools for understanding the resulting quiver gauge theories using exceptional collections. We prove two important results for a general quiver gauge theory: 1) we show the ordering of the nodes can be determined up to cyclic permutation and 2) we derive a simple formula for the ranks of the gauge groups (at the conformal point) in terms of the numbers of bifundamentals. We also provide a detailed analysis of four node quivers, examining when precisely mutations of the exceptional collection are related to Seiberg duality.