Abstract
We discuss the properties of massive type IIA flux compactifications. In particular, we investigate in which case one can obtain dS vacua at large volume and small coupling. We support a general discussion of scaling symmetries with the analysis of a concrete example. We find that the large volume and weak coupling limit requires a large number of O6-planes. Since these are bound for any given compactification space one cannot get arbitrarily good control over α′ and string loop corrections.
Highlights
The authors of [1] present a large number of explicit examples that satisfy the dS swampland conjecture
While there have been recent breakthroughs that show that the obstinate tachyon [76,77,78,79] in these dS critical points can be removed by including anti-D6-branes [80] or by adding KK monopoles [81], it remains unclear whether one can find dS vacua that are at large volume and weak coupling, i.e. that are in a regime in which we can trust the supergravity approximation
We want to address the important question, when can we find solutions at large volume and weak coupling, i.e. at ρ, τ 1? We have seen in the previous subsection that the large F4-flux limit that was present for AdS vacua obtained from compactifications on Calabi-Yau manifolds is obstructed in the presence of curvature
Summary
We discuss the scaling limits of the scalar potential that arises in flux compactifications of massive type IIA string theory. While the full scalar potential is rather complicated, one can learn already a lot by restricting to a two dimensional slice in moduli space that is spanned by the string coupling eφ and the internal volume V6. The term Asources arises from the DBI-terms integrated over the 3-cycles wrapped by these sources and has the following dependence on the number of O6-planes and D6-branes: Asources ∝ 2NO6 − ND6 − ND6. The suppressed prefactor is positive since (anti-)D-branes have positive tension and contribute positively to the scalar potential. AR6 ∝ −R6, arises from integrating the internal Ricci scalar over the internal space. It is positive, if the internal space is negatively curved and negative, if the internal space is positively curved
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