Towards Minkowski vacua in type II string compactifications

Abstract

We study the vacuum structure of compactifications of type II string theories on orientifolds with SU (3) × SU (3) structure. We argue that generalised geometry enables us to treat these non-geometric compactifications using a supergravity analysis in a way very similar to geometric compactifications. We find supersymmetric Minkowski vacua with all the moduli stabilised at weak string coupling and all the tadpole conditions satisfied. Generically the value of the moduli fields in the vacuum is parametrically controlled and can be taken to arbitrarily large values. † An example of a generalised almost complex structure is one induced by an almost complex structure IAnother example is one that is induced by an almost symplectic two-form JIn general, a generalised almost complex structure will be some combination of the two. Given a generalised almost complex structure it is possible to generate a new one by a B-transformation defined as 4) where B is a real two-form, B ∈ Λ 2 T * . Similarly we can also generate a new one through a β-transform 5)

Helical phase inflation via non-geometric flux compactifications: from natural to starobinsky-like inflation

“…The supersymmetric Minkowski vacuum and moduli stabilization from the Type IIB compactifications on orientifolds have been studied in refs. [61][62][63][64][65][66][67]. Most of these works targeted the compactification on isotropic T 6 , i.e., with an exchange symmetry among three sub-tori so that T 1 = T 2 = T 3 and U 1 = U 2 = U 3 .…”

“…Such compactifications have been studied in refs. [61][62][63][64][65][66][67][68][69] as a mechanism for obtaining vacua with full moduli stabilization. The authors of these works have mainly focused on the simplified case where an exchange symmetry exists among three sub-tori.…”

A ten-dimensional action for non-geometric fluxes

“…They are only defined up to [12,60,5,23,24] that the appearance of such a β block can be a sign of non-geometry. Before giving details on this point, let us mention that such a bivector first appeared in a particular…”

“…The NSNS degrees of freedom would be the only ones involved, but they would be mixed into new variables which would reveal non-geometric fluxes in the action. To find the good variables, we were inspired by the Generalized Complex Geometry (GCG) [21,22] approach, where a particular object has been related [12,5,23,24] to non-geometry: the antisymmetric bivector β mn . We come back to these ideas in detail in section 2.…”

“…5 From the relation (1.3), together with a definition of the dilatonφ that leaves the measure of the NSNS action invariant, we read off the change of variables from the fieldsĝ,B andφ to the fieldsg,β, andφ. It is then reasonable to assume that the NSNS Lagrangian can equally well be written in the new variables.…”