| 总结: | <p>The main topic of this thesis is to explore the consistency and structure of realistic, 4d vacua of String Theory through the AdS/CFT correspondence. As a first step, we investigate whether Swampland constraints on the low-energy dynamics of weakly coupled, moduli-stabilised string vacua in AdS can be related to inconsistencies of their putative holographic duals or, more generally, recast in terms of CFT data. We find that various swampland consistency constraints are equivalent to a negativity condition on the sign of certain mixed anomalous dimensions. This condition is similar to well-established CFT positivity bounds arising from causality and unitarity, but not known to hold in general. The studied scenarios include LVS, KKLT, the type IIA DGKT flux vacua and both perturbative and racetrack stabilisation. We also point out an intriguing connection to the Swampland Distance Conjecture, both in its original and refined versions. A second, unexpected consequence of this analysis is that the CFT data for some of these vacua takes a universal form, independent of the compactification details. For the type IIA examples, we then give a concise argument that supersymmetric AdS DGKT flux vacua on general Calabi-Yaus always have integer conformal dimensions for all low-lying scalar primaries in the dual CFT. These integers are independent of any compactification details, such as the background fluxes or triple intersection numbers of the compact manifold. We give a tentative discussion of the origin of these integers and effects that would modify these results.</p>
<p>In the last part of the thesis, we take a more phenomenological approach and study the overshoot problem in the context of post-inflationary string cosmology (in particular LVS). We show that in LVS, provided the existence of a large hierarchy between the inflationary and the weak scales, initial seed radiation will localize the system onto a tracker solution where the problem is solved. The consistency require- ment of ending in a stable vacuum containing the weak hierarchy therefore gives a preference for high inflationary scales – an anthropic argument, if one likes, for a large inflation/weak hierarchy. We discuss various origins (both universal and model- dependent) of the initial seed radiation, with a particular emphasis on the possibility of having an LVS fundamental string network.</p>
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