Asymmetric Orbifolds, Noncommutative Geometry and Type I String Vacua

TL;DR

This paper explores the structure of asymmetric orbifolds in string theory, revealing that consistent open string descriptions involve background gauge fields and noncommutative geometry, with applications to type I vacua.

Contribution

It introduces a method to derive noncommutative geometry on D-branes in asymmetric orbifolds using T-duality and asymmetric rotations, advancing understanding of open string boundary conditions.

Findings

Background gauge fields are necessary for consistent open string descriptions.

Noncommutative geometry naturally arises on D-branes with mixed boundary conditions.

Constructed asymmetric type I vacua with open strings requiring mixed boundary conditions.

Abstract

We investigate the D-brane contents of asymmetric orbifolds. Using T-duality we find that the consistent description of open strings in asymmetric orbifolds requires to turn on background gauge fields on the D-branes. We derive the corresponding noncommutative geometry arising on such D-branes with mixed Neumann-Dirichlet boundary conditions directly by applying an asymmetric rotation to open strings with pure Dirichlet or Neumann boundary conditions. As a concrete application of our results we construct asymmetric type I vacua requiring open strings with mixed boundary conditions for tadpole cancellation.