Perturbative string theory forbids de Sitter times closed manifold solutions under the assumption that the Euclidean sphere partition function receives a nonzero 1/G_N contribution.
On Cosmological Constants from alpha’-Corrections
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abstract
We examine to what extent perturbative alpha'-corrections can generate a small cosmological constant in warped string compactifications. Focusing on the heterotic string at lowest order in the string loop expansion, we show that, for a maximally symmetric spacetime, the alpha'-corrected 4D scalar potential has no effect on the cosmological constant. The only relevant terms are instead higher order products of 4D Riemann tensors, which, however, are found to vanish in the usual perturbative regime of the alpha'-expansion. The heterotic string therefore only allows for 4D Minkowski vacua to all orders in alpha', unless one also introduces string loop and/or nonperturbative corrections or allows for curvatures or field strengths that are large in string units. In particular, we find that perturbative alpha'-effects cannot induce weakly curved AdS_4 solutions.
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String theory imposes constraints on dark energy but permits various construction attempts for de Sitter vacua and single-field exponential quintessence models despite obstructions.
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de Sitter in String Theory vs. Gibbons & Hawking
Perturbative string theory forbids de Sitter times closed manifold solutions under the assumption that the Euclidean sphere partition function receives a nonzero 1/G_N contribution.
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Dark energy from string theory: an introductory review
String theory imposes constraints on dark energy but permits various construction attempts for de Sitter vacua and single-field exponential quintessence models despite obstructions.