Asymmetric orbifolds, non-geometric fluxes and non-commutativity in closed string theory

摘要

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 α′. Finally, we relate these asymmetric orbifold spaces to inherently stringy Scherk-Schwarz backgrounds and non-geometric fluxes.