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started something at quiver gauge theory; some very basic sentences on the Idea of it all, and some bare minimum of references.
This is a vast subject, and clearly that entry deserves to be expanded much further.
In the course of creating this I needed to create brief entries B-brane and exceptional collection.
added pointer to
So the derived category of coherent sheaves on the target space time has an “exceptional collection” of objects (aren’t these known as tilting objects/bundles?). Realising the endomorphism algebra of these objects as the path algebra of some quiver. Its not entirely clear to me how this quiver relates to do one “coming from” the quiver gauge theory. I may have misunderstood quite a lot however.
So the story is a variant of the K-theoretic McKay correspondence: A D-brane sitting at a suitable conal singularity in a CY variety carries a certain gauge theory on its worldvolume. Under suitable conditions, this is a quiver gauge theory for the same quiver as that whose derived category is equivalent to the derived category of coherent sheaves on the conal variety.
One place where this is stated well is the introduction of
One day our entry on quiver gauge theories should be turned into something more useful…
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