We present a general formalism for incorporating the string corrections in generalised geometry, which necessitates the extension of the generalised tangent bundle. Not only are such extensions obstructed, string symmetries and the existence of a welldefined effective action require a precise choice of the (generalised) connection. The action takes a universal form given by a generalised Lichnerowitz-Bismut theorem. As examples of this construction we discuss the corrections linear in α ′ in heterotic strings and the absence of such corrections for type II theories.

Motivated by the desire to do proper model building with D7-branes and fluxes, we study the motion of D7-branes on a Calabi-Yau orientifold from the perspective of F-theory. We consider this approach promising since, by working effectively with an elliptically fibred M-theory compactification, the explicit positioning of D7-branes by (M-theory) fluxes is straightforward. The locations of D7-branes are encoded in the periods of certain M-theory cycles, which allows for a very explicit understanding of the moduli space of D7-brane motion. The picture of moving D7-branes on a fixed underlying space relies on negligible backreaction, which can be ensured in Sen's weak coupling limit. However, even in this limit we find certain 'physics obstructions' which reduce the freedom of the D7-brane motion as compared to the motion of holomorphic submanifolds in the orientifold background. These obstructions originate in the intersections of D7-branes and O7-planes, where the type IIB coupling cannot remain weak. We illustrate this effect for D7-brane models on CP 1 × CP 1 (the Bianchi-Sagnotti-Gimon-Polchinski model) and on CP 2 . Furthermore, in the simple example of 16 D7-branes and 4 O7-planes on CP 1 (F-theory on K3), we obtain a completely explicit parameterization of the moduli space in terms of periods of integral M-theory cycles. In the weak coupling limit, D7-brane motion factorizes from the geometric deformations of the base space.

Using the embedding tensor formalism we give the general conditions for the existence of N = 1 vacua in spontaneously broken N = 2 supergravities. Our results confirm the necessity of having both electrically and magnetically charged multiplets in the spectrum, but also show that no further constraints on the special Kähler geometry of the vector multiplets arise. The quaternionic field space of the hypermultiplets must have two commuting isometries, and as an example we discuss the special quaternionic-Kähler geometries which appear in the low-energy limit of type II string theories. For these cases we find the general solution for stable Minkowski and AdS N = 1 vacua, and determine the charges in terms of the holomorphic prepotentials. We find that the string theory realisation of the N = 1 Minkowski vacua requires the presence of non-geometric fluxes, whereas they are not needed for the AdS vacua. We also argue that our results should hold in the presence of spacetime and worldsheet instanton corrections.

Abstract:We study AdS backgrounds of N = 4 supergravity in four space-time dimensions which preserve all sixteen supercharges. We show that the graviphotons have to form a subgroup of the gauge group that consists of an electric and a magnetic SO(3) + ×SO(3) − . Moreover, these N = 4 AdS backgrounds are necessarily isolated points in field space which have no moduli.

Abstract:We classify the N = 4 supersymmetric AdS 5 backgrounds that arise as solutions of five-dimensional N = 4 gauged supergravity. We express our results in terms of the allowed embedding tensor components and identify the structure of the associated gauge groups. We show that the moduli space of these AdS vacua is of the form SU(1, m)/ U(1) × SU(m) and discuss our results regarding holographically dual N = 2 SCFTs and their conformal manifolds.