We analyse type IIA Calabi-Yau orientifolds with background fluxes and D6-branes.Rewriting the F-term scalar potential as a bilinear in flux-axion polynomials yields a more efficient description of the Landscape of flux vacua, as they are invariant under the discrete shift symmetries of the 4d effective theory. In particular, expressing the extremisation conditions of the scalar potential in terms of such polynomials allows for a systematic search of vacua. We classify families of N = 0 Minkowski, N = 1 AdS and N = 0 AdS flux vacua, extending previous findings in the literature to the Calabi-Yau context. We compute the spectrum of flux-induced masses for some of them and show that they are perturbatively stable, and in particular find a branch of N = 0 AdS vacua where tachyons are absent. Finally, we extend this Landscape to the open string sector by including mobile D6-branes and their fluxes.2 Type IIA orientifolds with fluxes Type IIA flux compactifications constitute a very interesting sector of the string landscape, in the sense that from the classical flux potential one obtains both 4d Minkowski and AdS vacua, some with all moduli stabilised [1,2,5]. In the following we will focus on (massive) type IIA flux vacua whose internal geometry can be approximated by a Calabi-Yau orientifold, as assumed in [24] to derive the F-term potential used in [11]. 1 We then express the scalar potential in the factorised bilinear form of [25]. As pointed out in there, the bilinear form of the potential is independent on whether the background geometry is Calabi-Yau or not and, as it will be clear from the computations in the next section, so will be the strategy to extract the vacua from it. Type IIA on Calabi-Yau orientifoldsLet us consider type IIA string theory compactified on an orientifold of R 1,3 ×M 6 with M 6 a compact Calabi-Yau three-fold. More precisely, we take the standard orientifold quotient by Ω p (−) F L R [5,33-35], 2 with R an anti-holomorphic Calabi-Yau involution acting on the Kähler 2-form J and the holomorphic 3-form Ω as R(J) = −J and R(Ω) = Ω, respectively.In the absence of background fluxes, and neglecting worldsheet and D-brane instanton effects, dimensional reduction to 4d will yield several massless chiral fields, whose scalar components can be described as follows [24]. On the one hand, we have the complexified Kähler moduli T a = b a + it a defined throughwhere J is expressed in the Einstein frame and φ represents the ten-dimensional dilaton. The 2-form basis −2 s ω a correspond to harmonic representatives of the classes in 1 Using such potential to search for vacua is justified a posteriori, by arguing that the flux-induced scale can be made parametrically smaller than the Kaluza-Klein scale, in the same region where corrections to the potential can be neglected, see [11] and section 5.1. Therefore, even if in the presence of fluxes the compactification metric is not Calabi-Yau, it is expected that the fluxless Kähler potential is a good approximation to capture the 4d dynamics. See also [31,3...

In this work we study ten-dimensional solutions to type IIA string theory of the form AdS 4 × X 6 which contain orientifold planes and preserve N = 1 supersymmetry. In particular, we consider solutions which exhibit some key features of the four-dimensional DGKT proposal for compactifications on Calabi-Yau manifolds with fluxes, and in this sense may be considered their ten-dimensional uplifts. We focus on the supersymmetry equations and Bianchi identities, and find solutions to these that are valid at the twoderivative level and at first order in an expansion parameter which is related to the AdS cosmological constant. This family of solutions is such that the background metric is deformed from the Ricci-flat one to one exhibiting SU(3) × SU(3)-structure, and dilaton gradients and warp factors are induced.

We analyse the flux-induced scalar potential for type IIA orientifolds in the presence of p-form, geometric and non-geometric fluxes. Just like in the Calabi-Yau case, the potential presents a bilinear structure, with a factorised dependence on axions and saxions. This feature allows one to perform a systematic search for vacua, which we implement for the case of geometric backgrounds. Guided by stability criteria, we consider configurations with a particular on-shell F-term pattern, and show that no de Sitter extrema are allowed for them. We classify branches of supersymmetric and non-supersymmetric vacua, and argue that the latter are perturbatively stable for a large subset of them. Our solutions reproduce and generalise previous results in the literature, obtained either from the 4d or 10d viewpoint.