Titlebook: Dark Energy; From EFTs to Supergr Francesc Cunillera Book 2023 The Editor(s) (if applicable) and The Author(s), under exclusive license to

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,Introduction and?Motivations,Let us begin by considering the age-old question: . To answer it, we first consider the two underlying low-energy theories that string theory aims to reproduce at the four-dimensional classical level: the Standard Model (SM) and General Relativity (GR). These two theories have been extremely successful in the many decades since their inception.

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Corrections to?the?Supergravity Action in?Type IIBIn this chapter we describe the most common and best understood ways to break the no-scale structure for the tree-level scalar potential described in Chap.?.. Moduli stabilisation and the effects of perturbative and non-perturbative corrections to the tree-level action are best understood in type IIB supergravity.

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Gauss-Bonnet Curvature Corrections and?the?Absence of?de Sitter VacuaIn the previous chapter, we described a number of phenomenological impediments to quintessence model building. Many of the arguments we described rely on compactifications of string theory on Calabi-Yau manifolds, originally chosen to preserve some supersymmetry in the external space.

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Conclusions and?OutlooksIn this thesis, we began by developing the necessary mathematical machinery to understand Calabi-Yau compactifications and proceeded to study the perturbative tree-level type IIB supergravity action in Chap.?

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