Asymmetric Orbifolds, Non-Geometric Fluxes and Non-Commutativity in Closed String Theory

TL;DR

This paper constructs exactly solvable asymmetric orbifold models in closed string theory that exhibit non-commutativity in string coordinates, linking non-geometric fluxes and stringy backgrounds.

Contribution

It introduces a class of asymmetric Z_N-orbifold models with explicit non-commutative algebra and modular invariant partition functions, advancing understanding of non-geometric fluxes in string theory.

Findings

Explicit construction of modular invariant partition functions.

Derivation of exact non-commutative algebra in string coordinates.

Connection of orbifold models to non-geometric flux backgrounds.

Abstract

In this paper we consider a class of exactly solvable closed string flux backgrounds that exhibit non-commutativity in the closed string coordinates. They are realized in terms of freely-acting asymmetric Z_N-orbifolds, which are themselves close relatives of twisted torus fibrations with elliptic Z_N-monodromy (elliptic T-folds). We explicitly construct the modular invariant partition function of the models and derive the non-commutative algebra in the string coordinates, which is exact to all orders in {\alpha}'. Finally, we relate these asymmetric orbifold spaces to inherently stringy Scherk-Schwarz backgrounds and non-geometric fluxes.