Double field theory at SL(2) angles

An extended field theory is presented that captures the full SL(2) x O(6; 6 vertical bar n) duality group of four-dimensional half-maximal supergravities. The theory has section constraints whose two inequivalent solutions correspond to minimal D = 10 supergravity and chiral half-maximal D = 6 supergravity, respectively coupled to vector and tensor multi-plets. The relation with O(6; 6+n) (heterotic) double field theory is thoroughly discussed. Non-Abelian interactions as well as background fluxes are captured by a deformation of the generalised diffeomorphisms. Finally, making use of the SL(2) duality structure, it is shown how to generate gaugings with non-trivial de Roo-Wagemans angles via generalised Scherk-Schwarz ansaatze. Such gaugings allow for moduli stabilisation including the SL(2) dilaton.