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Azumaya-type noncommutative spaces and morphisms therefrom: Polchinski's D-branes in string theory from Grothendieck's viewpoint

Chien-Hao Liu Shing-Tung Yau

Mathematical Physics mathscidoc:1912.43591

arXiv preprint arXiv:0709.1515, 2007.9
We explain how Polchinski's work on D-branes re-read from a noncommutative version of Grothendieck's equivalence of local geometries and function rings gives rise to an intrinsic prototype definition of D-branes (of B-type) as an Azumaya-type noncommutative space. Several originally open-string induced properties of D-branes can be reproduced solely by this intrinsic definition. We study also the moduli space of D0-branes on a commutative target space in this setup. Some of its features resembles gas of D0-branes in Vafa's work.
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@inproceedings{chien-hao2007azumaya-type,
  title={Azumaya-type noncommutative spaces and morphisms therefrom: Polchinski's D-branes in string theory from Grothendieck's viewpoint},
  author={Chien-Hao Liu, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204308593474155},
  booktitle={arXiv preprint arXiv:0709.1515},
  year={2007},
}
Chien-Hao Liu, and Shing-Tung Yau. Azumaya-type noncommutative spaces and morphisms therefrom: Polchinski's D-branes in string theory from Grothendieck's viewpoint. 2007. In arXiv preprint arXiv:0709.1515. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204308593474155.
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