Abstract
In the context of realizing de Sitter vacua and the slow-roll inflation, several no-go conditions have been found in the framework of type IIA (generalized) flux compactifications. In this article, using our recently proposed $T$-dual dictionary [P. Shukla, A dictionary for the type II non-geometric flux compactifications, arXiv:1909.07391], we translate various such type IIA no-go conditions that subsequently lead to some interesting de Sitter no-go scenarios in the presence of (non)geometric fluxes on the dual type IIB side. We also present the relevance of using $K3/{\mathbb{T}}^{4}$-fibered Calabi Yau threefolds in order to facilitate one particular class of the de Sitter no-go conditions. This analysis helps in refining certain corners of the vast nongeometric flux landscape for the hunt of de Sitter vacua.
Highlights
Recent revival of the swampland conjecture [1,2] has boosted a huge amount of interest toward exploring theexistence of de Sitter vacua within a consistent theory of quantum gravity
Where the constant c is an order one quantity. This conjecture has been supported by several explicit computations in the context of attempts made for realizing classical de Sitter solutions and inflationary cosmology in the type II superstring flux compactifications [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23]
Note that all the type IIA no-go results in [5,6,8,15], which we Tdualize, are realized using the extremization conditions only in the “volume/dilaton” plane, and without taking into account the complex structure moduli sector. This illustrates that any claim of evading the no-go originated from the volume/ dilaton analysis should be checked by including all the remaining moduli. (iii) On the lines of classifying type IIA and type IIB models based on theirgeometric nature via turning on a certain set of fluxes at a time, we present an interesting recipe that corresponds to considering what we call some “special solutions” of the NS-NS Bianchi identities
Summary
Recent revival of the swampland conjecture [1,2] has boosted a huge amount of interest toward exploring the (non)existence of de Sitter vacua within a consistent theory of quantum gravity. (i) Our so-called “cohomology” or “symplectic” formulation of the scalar potential presented in [108] opens up the window to study the nongeometric models beyond the toroidal constructions, and enables one to explicitly translate any useful findings of one setup into its T-dual picture On these lines, we plan to T-dualize the several de Sitter nogo scenarios realized in some purely geometric type IIA frameworks [5,6,8,15]. Though we attempt to keep the article self-contained, we encourage the interested readers to follow the other relevant details if necessary, e.g., on the superpotential, D-terms, directly from [108]
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