Moduli stabilisation and applications in IIB string theory

Abstract

SummaryString compactifications represent the most promising approach towards unifying general relativity with particle physics. However, naive compactifications give rise to massless particles (moduli) which would mediate unobserved longrange forces, and it is therefore necessary to generate a potential for the moduli.In the introductory chapters I review this problem and recall how in IIB compactifications the dilaton and complex structure moduli can be stabilised by 3-form fluxes. There exist very many possible discrete flux choices which motivates the use of statistical techniques to analyse this discretuum of choices. Such approaches generate formulae predicting the distribution of vacua and I describe numerical tests of these formulae on the Calabi-Yau P 4[1,1,2,2,6] . Stabilising the Kähler moduli requires nonperturbative superpotential effects. I review the KKLT construction and explain why this must in general be supplemented with perturbative Kähler corrections. I show how the incorporation of such corrections generically leads to non-supersymmetric minima at exponentially large volumes, giving a detailed account of the α ′ expansion and its relation to Kähler corrections. I illustrate this with explicit computations for the 1,1,6,9] . The next part of the thesis examines phenomenological applications of this construction. I first describe how the magnitude of the soft supersymmetry parameters may be computed. In the large-volume models the gravitino mass and soft terms are volume-suppressed. As we naturally have V ≫ 1, this gives a dynamical solution of the hierarchy problem. I also demonstrate the existence of a fine structure in the soft terms, with gaugino masses naturally lighter than the gravitino mass by a factor ln M P m 3/2 . A second chapter gives a detailed analysis of the relationship of moduli stabilisation to the QCD axions relevant to the strong CP problem, proving a no-go theorem on the compatibility of a QCD axion with supersymmetric moduli stabilisation. I describe how QCD axions can coexist with nonsupersymmetric perturbative stabilisation and how the large-volume models naturally contain axions with decay constants that are phenomenologically allowed and satisfy the appealing relationship f 2 a ∼ M P M susy . A further chapter describe how a simple and predictive inflationary model can be built in the context of the above large-volume construction, using the no-scale Kähler potential to avoid the η problem.I finally conclude, summarising the phenomenological scenario and outlining the prospects for future work.

Inflation and String Theory

“…where c is a constant (see [319]). Since G 3 depends on the dilaton and Ω involves the complex structure moduli, the superpotential (3.94) leads to a non-trivial potential for these moduli.…”

“…One might suspect from (3.108) that A ∝ M 3 KK , but because M KK /M pl depends on T +T , such a dependence would not be holomorphic. Instead, for typical complex structure moduli vevs and Dbrane positions, one has A ∼ M 3 pl : see [34,319]. A very similar superpotential contribution arises if Σ 4 is wrapped not by spacetime-filling D7-branes, but by Euclidean D3-branes, also known as D3-brane instantons [337] (see [338] for a review).…”

“…When the compactification volume is exponentially large, as in the large volume scenario [319,357], then a considerable number of corrections to the effective action in the α and string coupling expansions can be ignored. In particular, it has been argued that only a subset of the terms arising at order (α ) 3 make leading contributions.…”

“…The most concrete models of Kähler moduli inflation have been constructed in the Large Volume Scenario (LVS) [319]. 70 We reviewed LVS compactifications in §3.3.3.…”

Sparticle spectra and LHC signatures for large volume string compactifications

“…They have been applied to obtain string theory inflation [17], natural QCD axions [18], the scale for neutrino masses [19] and to low energy supersymmetric phenomenology [10 -13] in which they provide a natural hierarchy for supersymmetry breaking with the large volume leading to an intermediate string scale. A comprehensive review is [20]. We start by reviewing their construction and properties.…”