The NSNS Lagrangian of ten-dimensional supergravity is rewritten via a change of field variables inspired by Generalized Complex Geometry. We obtain a new metric and dilaton, together with an antisymmetric bivector field which leads to a ten-dimensional version of the non-geometric Q-flux. Given the involved global aspects of non-geometric situations, we prescribe to use this new Lagrangian, whose associated action is well-defined in some examples investigated here. This allows us to perform a standard dimensional reduction and to recover the usual contribution of the Q-flux to the four-dimensional scalar potential. An extension of this work to include the R-flux is discussed. The paper also contains a brief review on non-geometry.Comment: 47 pages; v2: minor modifications, references added, version to be published in JHE

In this paper we propose ten‐dimensional realizations of the non‐geometric fluxes Q and R. In particular, they appear in the NSNS Lagrangian after performing a field redefinition that takes the form of a T‐duality transformation. Double field theory simplifies the computation of the field redefinition significantly, and also completes the higher‐dimensional picture by providing a geometrical role for the non‐geometric fluxes once the winding derivatives are taken into account. The relation to four‐dimensional gauged supergravities, together with the global obstructions of non‐geometry, are discussed.

In this paper we investigate the connection between (non-)geometry and (non-)commutativity of the closed string. To this end, we solve the classical string on three T-dual toroidal backgrounds: a torus with H-flux, a twisted torus and a non-geometric background with Q-flux. In all three situations we work under the assumption of a dilute flux and consider quantities to linear order in the flux density. Furthermore, we perform the first steps of a canonical quantization for the twisted torus, to derive commutators of the string expansion modes. We use them as well as T-duality to determine, in the non-geometric background, a commutator of two string coordinates, which turns out to be non-vanishing. We relate this non-commutativity to the closed string boundary conditions, and the non-geometric Q-flux.

We give a geometrical interpretation of the nongeometric Q and R fluxes. To this end, we consider double field theory in a formulation that is related to the conventional one by a field redefinition taking the form of a T duality inversion. The R flux is a tensor under diffeomorphisms and satisfies a nontrivial Bianchi identity. The Q flux can be viewed as part of a connection that covariantizes the winding derivatives with respect to diffeomorphisms. We give a higher-dimensional action with a kinetic term for the R flux and a "dual" Einstein-Hilbert term containing the connection Q.

Recently, it has become clear that neighboring multiple vacua might have interesting consequences for the physics of the early universe. In this paper we investigate the topography of the string landscape corresponding to complex structure moduli of flux compactified type IIB string theory. We find that series of continuously connected vacua are common. The properties of these series are described, and we relate the existence of infinite series of minima to certain unresolved mathematical problems in group theory. Numerical studies of the mirror quintic serve as illustrating examples.

We examine compactifications of heterotic string theory on manifolds with SU (3) structure. In particular, we study N = 1/2 domain wall solutions which correspond to the perturbative vacua of the 4D, N = 1 supersymmetric theories associated to these compactifications. We extend work which has appeared previously in the literature in two important regards. Firstly, we include two additional fluxes which have been, heretofore, omitted in the general analysis of this situation. This allows for solutions with more general torsion classes than have previously been found. Secondly, we provide explicit solutions for the fluxes as a function of the torsion classes. These solutions are particularly useful in deciding whether equations such as the Bianchi identities can be solved, in addition to the Killing spinor equations themselves. Our work can be used to straightforwardly decide whether any given SU (3) structure on a six-dimensional manifold is associated with a solution to heterotic string theory. To illustrate how to use these results, we discuss a number of examples taken from the literature.

Three-dimensional smooth, compact toric varieties (SCTV), when viewed as real six-dimensional manifolds, can admit G-structures rendering them suitable for internal manifolds in supersymmetric flux compactifications. We develop techniques which allow us to systematically construct G-structures on SCTV and read off their torsion classes. We illustrate our methods with explicit examples, one of which consists of an infinite class of toric CP 1 bundles. We give a self-contained review of the relevant concepts from toric geometry, in particular the subject of the classification of SCTV in dimensions ≤ 3. Our results open up the possibility for a systematic construction and study of supersymmetric flux vacua based on SCTV.

We consider the non-perturbative superpotential for a class of four-dimensional N = 1 vacua obtained from M-theory on seven-manifolds with holonomy G 2 . The class of G 2 -holonomy manifolds we consider are so-called twisted connected sum (TCS) constructions, which have the topology of a K3-fibration over S 3 . We show that the non-perturbative superpotential of M-theory on a class of TCS geometries receives infinitely many inequivalent M2-instanton contributions from infinitely many three-spheres, which we conjecture are supersymmetric (and thus associative) cycles. The rationale for our construction is provided by the duality chain of [1], which relates M-theory on TCS G 2 -manifolds to E 8 × E 8 heterotic backgrounds on the Schoen Calabi-Yau threefold, as well as to F-theory on a K3-fibered Calabi-Yau fourfold. The latter are known to have an infinite number of instanton corrections to the superpotential and it is these contributions that we trace through the duality chain back to the G 2 -compactification.1 These also have an interpretation as the type IIB string compactified on the base of the elliptic fibration, with the fibers specifying the variable axio-dilaton field, see, e.g., [2].