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

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

Gauged supergravities and non-geometric Q/R-fluxes from asymmetric orbifold CFT’s

“…However, from the lower-dimensional point of view, such gaugings of supergravity do exist and can also be realized in the full string theory. For instance, a compactification with (elliptic) duality twists can be described at particular points of the moduli space by a freely-acting asymmetric orbifold [43], hence, providing a string realization of a Q-background. The presence of the Q-flux is associated to the asymmetry in the generalized fiber of the compactification.…”

“…This class of orbifolds was later generalized to asymmetric versions in [43] and we will adopt the notation of the latter. For the purposes of the discussion, we will factorize the fiber T 5 as T 4 × S 1 ′ , with S 1 ′ being a spectator circle, so that the orbifold acts symmetrically on the left-and rightmoving T 4 × S 1 coordinates:…”

Matrix theory origins of non-geometric fluxes

“…Such structures were also derived using conformal field theory in Ref. [57] and later also appeared in the context of asymmetric orbifolds [58].…”

Non-geometric backgrounds based on topological interfaces

“…The non-geometric backgrounds involving the duality twist generally lie at the fixed points of moduli, and the CFT description there is expected to be given by certain asymmetric orbifolds [1]. Along this line, the T-folds with or without non-geometric fluxes have been studied by means of the world-sheet approaches, e.g., in [9][10][11][12][13].…”

“…Taking also into account our motivation to discuss possible roles of the world-sheet interfaces for string theory, our models may be the simplest from our point of view. Compared with the preceding works [9][10][11][12][13], where the exact CFT partition functions for T-folds are constructed by identifying some asymmetric twists with particular T-duality transformations, our construction takes a different route based on the interfaces. In the case of the group-like defect, our resultant model, however, fits into the same category of asymmetric orbifolds, except that our model has a continuous modulus in a fixed line instead of isolated fixed points.…”