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Mathematics > Algebraic Geometry

arXiv:0709.1515 (math)
[Submitted on 11 Sep 2007]

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

Authors:Chien-Hao Liu, Shing-Tung Yau
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Abstract: 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.
Comments: 57 pages
Subjects: Algebraic Geometry (math.AG); High Energy Physics - Theory (hep-th); Symplectic Geometry (math.SG)
MSC classes: 14A22, 81T30
Cite as: arXiv:0709.1515 [math.AG]
  (or arXiv:0709.1515v1 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.0709.1515

Submission history

From: Chien-Hao Liu [view email]
[v1] Tue, 11 Sep 2007 01:17:57 UTC (92 KB)
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