Abstract
We review recent attempts to try to combine global issues of string compactifications, like moduli stabilisation, with local issues, like semi–realistic D–brane constructions. We list the main problems encountered, and outline a possible solution which allows globally consistent embeddings of chiral models. We also argue that this stabilisation mechanism leads to an axiverse. We finally illustrate our general claims in a concrete example where the Calabi–Yau manifold is explicitly described by toric geometry.
Highlights
Two longstanding problems of string compactifications are moduli stabilisation and the derivation of realistic D-brane models
We focus on type IIB/F-theory compactifications with D3/D7-branes and O3/O7-planes where the compact Calabi-Yau three-fold can be explicitly described in terms of toric geometry [4]
Our strategy to overcome this problem is the simplest one: fix the T -moduli by only one nonperturbative effect. This leads to the LARGE Volume Scenario (LVS) where the presence of just a single diagonal del Pezzo with non-perturbative effects is enough to ensure the stabilisation of the Calabi-Yau volume by setting W0 ∼ O(1) and exploiting α′-corrections to K [10]
Summary
Two longstanding problems of string compactifications are moduli stabilisation and the derivation of realistic D-brane models. D-branes provide non-Abelian gauge bosons whereas, on the other side, local sources allow to evade no-go theorems which prevent the turning on of background fluxes. These fluxes generate a potential for most of the moduli. In this brane-world scenario, finding a solution to these two crucial problems seems to be somewhat easier since moduli fixing is a global issue whereas model building is a local issue. The main goal is to overcome these difficulties keeping control over the 4D supergravity theory and stabilising the moduli inside the Kahler cone Another non-trivial requirement is getting, at the same time, an interesting particle phenomenology and cosmology. Our model is able to reproduce a visible sector gauge coupling of the correct size and interesting phenomenological scales like TeV-scale supersymmetry and an intermediate scale decay constant for the QCD axion (realised as a local closed string mode, see [8]) for natural values of the underlying parameters
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