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

TL;DR

This paper explores the connection between geometric and non-geometric fluxes in string theory compactifications using asymmetric orbifold conformal field theories, providing a systematic method to derive gauge algebras and analyze flux transformations under T-duality.

Contribution

It introduces a general procedure for deriving gauge algebras from exact CFT descriptions of orbifolds, linking asymmetry to non-geometric fluxes and analyzing their T-duality transformations.

Findings

Identified fluxes in symmetric and asymmetric orbifolds.

Derived flux backgrounds including geometric, Q, and R fluxes.

Presented an example with all fluxes turned on simultaneously.

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 Z4xZ2 orbifold in which all geometric and non-geometric fluxes {\omega}, 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 simultaneously depend non-trivially on both the coordinates and their winding T-duals.