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R. Kallosh, A. Linde, C. Roupec:
"de Sitter Minima from M theory and String theory";
Physical Review D, 101 (2020), 4; 046018-1 - 046018-8.

We study M-theory compactification on T7/Z23 in the presence of a seven-flux, metric fluxes, and KK monopoles. The effective four-dimensional supergravity has seven chiral multiplets whose couplings are specified by the G2-structure of the internal manifold. We supplement the corresponding superpotential by a KKLT type nonperturbative exponential contribution for all, or for some of the seven moduli, and find a discrete set of supersymmetric Minkowski minima. We also study type IIA and type IIB string theory compactified on T6/Z22. In type IIA, we use a six-flux, geometric fluxes, and nonperturbative exponents. In type IIB theory, we use F and H fluxes, and nongeometric Q and P fluxes, corresponding to consistently gauged supergravity with certain embedding tensor components, without nonperturbative exponents. Also in these situations, we produce discrete Minkowski minima. Finally, to construct dS vacua starting from these Minkowski progenitors, we follow the procedure of mass production of dS vacua.

de Sitter minima, supergravity

http://dx.doi.org/10.1103/PhysRevD.101.046018