We show that one can find de Sitter critical points (saddle points) in models of flux compactification of Type IIB String Theory without any uplifting terms and in the presence of several moduli. We demonstrate this by giving explicit examples following some of the ideas recently presented by Conlon in ref.[1], as well as more generic situations where one can violate the strong form of the de Sitter Swampland Conjecture. We stabilize the complex structure and the dilaton with fluxes, and we introduce a racetrack potential that fixes the Kähler moduli. The resultant potentials generically exhibit de Sitter critical points and satisfy several consistency requirements such as flux quantization, large internal volume, and weak coupling, as well as a form of the so-called Weak Gravity Conjecture. Furthermore, we compute the form of the potential around these de Sitter saddle points and comment on these results in connection to the refined and more recent version of the de Sitter Swampland Conjecture.

The large number of moduli fields arising in a generic string theory compactification makes a complete computation of the low energy effective theory infeasible. A common strategy to solve this problem is to consider Calabi-Yau manifolds with discrete symmetries, which effectively reduce the number of moduli and make the computation of the truncated Effective Field Theory possible. In this approach, however, the couplings (e.g., the masses) of the truncated fields are left undetermined. In the present paper we discuss the tree-level mass spectrum of type-IIB flux compactifications at Large Complex Structure, focusing on models with a reduced one-dimensional complex structure sector. We compute the tree-level spectrum for the dilaton and complex structure moduli, including the truncated fields, which can be expressed entirely in terms of the known couplings of the reduced theory. We show that the masses of this set of fields are naturally heavy at vacua consistent with the KKLT construction, and we discuss other phenomenologically interesting scenarios where the spectrum involves fields much lighter than the gravitino. We also derive the probability distribution for the masses on the ensemble of flux vacua, and show that it exhibits universal features independent of the details of the compactification. We check our results on a large sample of flux vacua constructed in an orientifold of the Calabi-Yau $$ {\mathbbm{W}\mathrm{\mathbb{P}}}_{\left[1,1,1,1,4\right]}^4 $$ W ℙ 1 1 1 1 4 4 . Finally, we also discuss the conditions under which the spectrum derived here could arise in more general compactifications.

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Phenomenologically interesting scalar potentials are highly atypical in generic random landscapes. We develop the mathematical techniques to generate constrained random potentials, i.e. Slepian models, which can globally represent low-probability realizations of the landscape. We give analytical as well as numerical methods to construct these Slepian models for constrained realizations of a full Gaussian random field around critical as well as inflection points. We use these techniques to numerically generate in an efficient way a large number of minima at arbitrary heights of the potential and calculate their non-perturbative decay rate. Furthermore, we also illustrate how to use these methods by obtaining statistical information about the distribution of observables in an inflationary inflection point constructed within these models.

We analyze the tree-level potential of type IIB flux compactifications in warped Calabi-Yau orientifolds, in regions of weak coupling and moderately large complex structure. In this regime, one may approximate the flux-induced superpotential W by a polynomial on the axio-dilaton and complex structure fields, and a significant fraction of vacua corresponds to a quadratic W. In this quadratic case, we argue that vacua fall into three classes, for which one can push the analytic description of their features. In particular, we provide analytic expressions for the vacuum expectation values and flux-induced masses of the axio-dilaton and complex structure fields in a large subclass of vacua, independently of the Calabi-Yau and the number of moduli. We show that supersymmetric vacua always contain flat directions, at least at this level of approximation. Our findings allow to generate vast ensembles of flux vacua in specific Calabi-Yau geometries, as we illustrate in a particular example.