26 research outputs found
Exceptional Collections and del Pezzo Gauge Theories
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.Comment: 26 pages, 1 figure; v2 footnote 2 amended; v3 ref adde