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

TL;DR

This paper reinterprets Polchinski's D-branes within a noncommutative algebraic geometry framework, specifically using Azumaya-type spaces, to provide an intrinsic, algebraic definition and explore their moduli spaces.

Contribution

It introduces an intrinsic algebraic definition of B-type D-branes as Azumaya noncommutative spaces based on Grothendieck's local geometry equivalence.

Findings

Reproduces key properties of D-branes through the intrinsic definition.

Studies the moduli space of D0-branes, revealing features similar to gas of D0-branes.

Provides a noncommutative geometric perspective on D-branes in string theory.

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.