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Azumaya structure on D-branes and deformations and resolutions of a conifold revisited: Klebanov-Strassler-Witten vs. Polchinski-Grothendieck

Chien-Hao Liu Shing-Tung Yau

Mathematical Physics mathscidoc:1912.43662

arXiv preprint arXiv:0907.0268, 2009.7
In this sequel to [L-Y1],[LLSY], and [L-Y2](respectively arXiv: 0709.1515 [math. AG], arXiv: 0809.2121 [math. AG], and arXiv: 0901.0342 [math. AG]), we study a D-brane probe on a conifold from the viewpoint of the Azumaya structure on D-branes and toric geometry. The details of how deformations and resolutions of the standard toric conifold Y can be obtained via morphisms from Azumaya points are given. This should be compared with the quantum-field-theoretic/D-brany picture of deformations and resolutions of a conifold via a D-brane probe sitting at the conifold singularity in the work of Klebanov and Witten [KW](arXiv: hep-th/9807080) and Klebanov and Strasser [KS](arXiv: hep-th/0007191). A comparison with resolutions via noncommutative desingularizations is given in the end.
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@inproceedings{chien-hao2009azumaya,
  title={Azumaya structure on D-branes and deformations and resolutions of a conifold revisited: Klebanov-Strassler-Witten vs. Polchinski-Grothendieck},
  author={Chien-Hao Liu, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204817060944226},
  booktitle={arXiv preprint arXiv:0907.0268},
  year={2009},
}
Chien-Hao Liu, and Shing-Tung Yau. Azumaya structure on D-branes and deformations and resolutions of a conifold revisited: Klebanov-Strassler-Witten vs. Polchinski-Grothendieck. 2009. In arXiv preprint arXiv:0907.0268. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204817060944226.
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