Exceptional Collections and del Pezzo Gauge Theories

Abstract

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.

26 pages, 1 figure; v2 footnote 2 amended; v3 ref added

References in corpus (6)

• The Exact Superconformal R-Symmetry Maximizes a
• Central Charges and $U(1{)}_R$ Symmetries in $\mathcal{N}=1$ Super Yang-Mills
• Dibaryons from Exceptional Collections
• Dibaryon Spectroscopy
• Baryon Charges in 4d Superconformal Field Theories and Their AdS Duals
• Seiberg duality as derived equivalence for some quiver gauge theories

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