Abstract
Abstract We investigate the orbifold limits of string theory compactifications with geometric and non-geometric fluxes. Exploiting the connection between internal fluxes and structure constants of the gaugings in the reduced supergravity theory, we can identify the types of fluxes arising in certain classes of freely-acting symmetric and asymmetric orbifolds. We give a general procedure for deriving the gauge algebra of the effective gauged supergravity using the exact CFT description at the orbifold point. We find that the asymmetry is, in general, related to the presence of non-geometric Q- and R- fluxes. The action of T-duality is studied explicitly on various orbifold models and the resulting transformation of the fluxes is derived. Several explicit examples are provided, including compactifications with geometric fluxes, Q-backgrounds (T-folds) and R-backgrounds. In particular, we present an asymmetric $ {{\mathbb{Z}}_4} $ × $ {{\mathbb{Z}}_2} $ orbifold in which all geometric and non-geometric fluxes ω, H, Q, R are turned on simultaneously. We also derive the corresponding flux backgrounds, which are not in general T-dual to geometric ones, and may even simul-taneously depend non-trivially on both the coordinates and their winding T-duals.
Highlights
String theory provides a framework in which the concepts of classical geometry are generalized in rather intriguing ways
We investigate the orbifold limits of string theory compactifications with geometric and non-geometric fluxes
The fully-fledged string theory is described in terms of an exact conformal field theory (CFT)
Summary
String theory provides a framework in which the concepts of classical geometry are generalized in rather intriguing ways. In this way, we derive novel, more general non-geometric T-fold backgrounds with Qand even R-fluxes that are not T-dual to any geometric compactification, since the corresponding asymmetric orbifolds are not T-dualizable to any symmetric orbifold construction. The method of providing the map from the orbifold CFT’s to the T-folds with non-constant background fields G, B, relies in the faithful embedding of the discrete orbifold group M × Minto the O(d, d) duality group that acts on the background parameters G, B of the fiber space Using this information, one may derive the modular transformation rules of the fiber background fields, as one encircles the base coordinate X. In the more general case of combined momentum and winding shifts, the fiber background depends on both the base coordinate and its dual, G(X, X ), B(X, X )
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