By implementing a genetic algorithm we search for stable vacua in Type IIB nongeometric flux compactification on an isotropic torus with orientifold 3-planes. We find that the number of stable dS and AdS vacua are of the same order. Moreover we find that in all dS vacua the multi-field slow-roll inflationary conditions are fulfilled. Specifically we observe that inflation is driven by the axio-dilaton and the Kähler moduli. We also comment on the existence of one stable dS vacuum in the presence of exotic orientifolds. 1 cesaredas@fisica.ugto.mx 2 luisreydb@fisica.ugto.mx 3 oloaiza@fisica.ugto.mx 4 msabido@fisica.ugto.mx 1 arXiv:1302.0529v3 [hep-th] 10 Nov 2013Recently, there has been a huge interest in the search for classical de Sitter (dS) vacua within the context of superstring compactification. In the last few years, some constraints have been imposed by estimating the contributions to the effective scalar potential from each of the components that play a role in the compactification process. For instance, there is a no-go theorem, indicating that the existence of dS vacua in compactifications threaded with standard NS-NS and R-R fluxes is incompatible with inflation[1]. Recently, in the context of these standar type IIB compactifications, it has been shown the existence of classical dS vacua in specific and suitable D-brane configurations with orientifold planes [2][3][4]. On the other hand, further studies show that by considering a bigger set of allowed fluxes and more general structures for the internal geometry, it is possible to find some stable dS vacua [5][6][7][8][9][10][11][12][13][14][15][16][17][18] although their compatibility with inflation has not been studied in detail. In this work we present some stable dS vacua consistent with inflation.There are some essential ingredients string compactifications should contain to enhance the chances of finding stable dS vacua: a negative curved internal manifold and a small number of moduli fields [19][20][21].Here, we take the approach consisting in computing the scalar potential from a superpotential with all the above features. Specifically, a compactification on a negatively curved manifold with a superpotential W that depends at tree level on a small set of moduli is achieved by considering a type II string compactification on a six-dimensional isotropic torus in the presence of non-geometric fluxes [22][23][24][25]. (2.12) where J = (j±, k) and M = (m±). The Bianchi identity Q · H 3 = 0 decomposes as A M J · A M J = (A M J ) δ (A M J ) λ η δλ = 0, (2.13) for j = j , diag(η) = {−1, 1, 1, 1} and for the combinations M = (0+), J = {(2, 0+), (1, 3−)} and M = (3−), J = {(1, 2−), (2, 1+)}, while Q · Q = 0 decomposes as,

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Non-geometric flux-scaling vacua provide promising starting points to realize axion monodromy inflation via the F-term scalar potential. We show that these vacua can be uplifted to Minkowski and de Sitter by adding an D3-brane or a D-term containing geometric and non-geometric fluxes. These uplifted non-supersymmetric models are analyzed with respect to their potential to realize axion monodromy inflation self-consistently. Admitting rational values of the fluxes, we construct examples with the required hierarchy of mass scales.

We construct non-perturbatively exact four-dimensional Minkowski vacua of type IIB string theory with non-trivial fluxes. These solutions are found by gluing together, consistently with U-duality, local solutions of type IIB supergravity on $T^4 \times \mathbb{C}$ with the metric, dilaton and flux potentials varying along $\mathbb{C}$ and the flux potentials oriented along $T^4$. We focus on solutions locally related via U-duality to non-compact Ricci-flat geometries. More general solutions and a complete analysis of the supersymmetry equations are presented in the companion paper [1]. We build a precise dictionary between fluxes in the global solutions and the geometry of an auxiliary $K3$ surface fibered over $\mathbb{CP}^1$. In the spirit of F-theory, the flux potentials are expressed in terms of locally holomorphic functions that parametrize the complex structure moduli space of the $K3$ fiber in the auxiliary geometry. The brane content is inferred from the monodromy data around the degeneration points of the fiber.Comment: 55 pages, including 4 appendices and many colour figure

We find analytic solutions of type IIB supergravity on geometries that locally take the form Mink×M 4 ×C with M 4 a generalised complex manifold. The solutions involve the metric, the dilaton, NSNS and RR flux potentials (oriented along the M 4 ) parametrised by functions varying only over C. Under this assumption, the supersymmetry equations are solved using the formalism of pure spinors in terms of a finite number of holomorphic functions. Alternatively, the solutions can be viewed as vacua of maximally supersymmetric supergravity in six dimensions with a set of scalar fields varying holomorphically over C. For a class of solutions characterised by up to five holomorphic functions, we outline how the local solutions can be completed to four-dimensional flux vacua of type IIB theory. A detailed study of this global completion for solutions with two holomorphic functions has been carried out in the companion paper [1]. The fluxes of the global solutions are, as in F-theory, entirely codified in the geometry of an auxiliary K3 fibration over CP 1 . The results provide a geometric construction of fluxes in F-theory.

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Based on the flux‐scaling scenario we study a model consisting on Type IIB string theory compactified on a Calabi‐Yau manifold with a frozen complex structure in the presence of generic fluxes. The model contains (meta)stable Minkowski and de Sitter vacua as well as inflationary directions driven by two independent linear combination of axions. Due to a numerical control by fluxes, we show that cosmological parameters as the spectral index, tensor‐to‐scalar ratio and non‐Gaussianities can be kept within observed bounds while preserving the desired hierarchies on physical scales. Moreover we compute the deviation of the inflationary trajectories from geodesics on field space in terms of the fluxes showing that for some regions, they fulfill the recent proposed swampland criterion for multi‐field scenarios.

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