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

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.

57 pages

References in corpus (6)

• D-branes and K-theory in 2D topological field theory
• Stability conditions on triangulated categories
• Transformation of algebraic Gromov-Witten invariants of three-folds under flops and small extremal transitions, with an appendix from the stringy and the symplectic viewpoint
• Three talks on noncommutative geometry@n
• Symmetric product as moduli space of linear representations
• Degeneration and gluing of Kuranishi structures in Gromov-Witten theory and the degeneration/gluing axioms for open Gromov-Witten invariants under a symplectic cut

Cited by in corpus (4)

• Morphisms from Azumaya prestable curves with a fundamental module to a projective variety: Topological D-strings as a master object for curves
• Azumaya structure on D-branes and resolution of ADE orbifold singularities revisited: Douglas-Moore vs. Polchinski-Grothendieck
• Nontrivial Azumaya noncommutative schemes, morphisms therefrom, and their extension by the sheaf of algebras of differential operators: D-branes in a $B$-field background à la Polchinski-Grothendieck Ansatz
• Azumaya structure on D-branes and deformations and resolutions of a conifold revisited: Klebanov-Strassler-Witten vs. Polchinski-Grothendieck