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arXiv · 0901.0342

Azumaya structure on D-branes and resolution of ADE orbifold singularities revisited: Douglas-Moore vs. Polchinski-Grothendieck

Chien-Hao Liu·Shing-Tung Yau
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Abstract

In this continuation of [L-Y1] and [L-L-S-Y], we explain how the Azumaya structure on D-branes together with a netted categorical quotient construction produces the same resolution of ADE orbifold singularities as that arises as the vacuum manifold/variety of the supersymmetric quantum field theory on the D-brane probe world-volume, given by Douglas and Moore [D-M] under the string-theory contents and constructed earlier through hyper-Kähler quotients by Kronheimer and Nakajima. This is consistent with the moral behind this project that Azumaya-type structure on D-branes themselves -- stated as the Polchinski-Grothendieck Ansatz in [L-Y1] -- gives a mathematical reason for many originally-open-string-induced properties of D-branes.

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Chien-Hao Liu, Shing-Tung Yau. 2009-01-03. Azumaya structure on D-branes and resolution of ADE orbifold singularities revisited: Douglas-Moore vs. Polchinski-Grothendieck. https://arxiv.org/abs/0901.0342

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