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arXiv · 1112.4317

Azumaya noncommutative geometry and D-branes - an origin of the master nature of D-branes

Chien-Hao Liu
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Abstract

In this lecture I review how a matrix/Azumaya-type noncommutative geometry arises for D-branes in string theory and how such a geometry serves as an origin of the master nature of D-branes; and then highlight an abundance conjecture on D0-brane resolutions of singularities that is extracted and purified from a work of Douglas and Moore in 1996. A conjectural relation of our setting with `D-geometry' in the sense of Douglas is also given. The lecture is based on a series of works on D-branes with Shing-Tung Yau, and in part with Si Li and Ruifang Song.

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Chien-Hao Liu. 2011-12-19. Azumaya noncommutative geometry and D-branes - an origin of the master nature of D-branes. https://arxiv.org/abs/1112.4317

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