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nLab > Latest Changes: quiver gauge theory

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMay 27th 2014

    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.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJan 20th 2019
    • (edited Jan 20th 2019)

    added pointer to

    diff, v10, current

    • CommentRowNumber3.
    • CommentAuthorAli Caglayan
    • CommentTimeJan 21st 2019

    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.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJan 22nd 2019

    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

    • Aaron Bergman, Nicholas J. Proudfoot, “Moduli Spaces for D-branes at the Tip of a Cone” (arXiv:hep-th/0510158)

    One day our entry on quiver gauge theories should be turned into something more useful…

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJan 22nd 2019
    • (edited Jan 22nd 2019)

    [ removed ]

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