Moduli Stabilisation and Applications in IIB String Theory

TL;DR

The thesis investigates moduli stabilisation in IIB string theory, emphasizing flux-induced fixing of the dilaton and complex structure and the necessity of including perturbative Kahler corrections to achieve controlled minima. It introduces and analyzes the Large Volume Scenario, where nonperturbative Kahler effects combined with alpha' corrections yield non-supersymmetric AdS minima at exponentially large volumes, with distinctive hierarchies among moduli and a calculable soft- SUSY-breaking structure. The work tests statistical predictions for flux vacua distributions, provides explicit model calculations (notably for P^4_{[1,1,2,2,6]} and P^4_{[1,1,1,6,9]}), and derives predictions for low-energy phenomenology, including gaugino and scalar masses for D3/D7-brane visible sectors and implications for axions and inflation. Together these results offer a comprehensive framework linking string-scale physics to potential experimental signatures via moduli spectra, soft terms, and cosmological implications, while highlighting the robustness and distinct phenomenology of LVS compared to KKLT vacua.

Abstract

This article represents the author's PhD thesis. It describes moduli stabilisation in IIB string theory and applications to phenomenological topics. The first half of the thesis starts with an introductory review. It continues with an account of the statistics of complex structure moduli stabilisation before moving to Kahler moduli stabilisation. It describes in detail the large-volumes models and justifies the assumptions used in their construction. The second half of the thesis is concerned with applications to phenomenological topics. These include supersymmetry breaking and soft terms, inflationary model building and axions.

Figures (14)

• Figure 1: The Higgs mass is radiatively unstable in the Standard Model due to quadratic divergences from top loops.
• Figure 2: Number of vacua with $\vert \psi \vert < r$. The value of $N$ plotted includes a weighting due to the $SL(2,\mathbb{Z})$ copies of each vacuum within the range of fluxes sampled. The dots represent the numerical results, and the continuous line the (rescaled) numerical integration of $\int_{\vert \psi \vert < r} d \mu$, where $d \mu$ is the index density. The flux range used was (-20,20).
• Figure 3: The weighted number of vacua, $N$, with $\vert \phi \vert < r$. The dots represent the numerical results and the continuous line the numerical integration of $\int_{\vert \phi \vert < r} d \mu$, rescaled by the same factor as in diagram \ref{['psismallresults']}.
• Figure 4: The weighted number of vacua $N$ with $N_{flux} < L$. $4.5 \times 10^6$ sets of flxues were generated, with values of $L$ equally distributed between $0$ and $800$ and the range of fluxes being $(-20,20)$. The results are fit by $N \sim L^{4.3}$.
• Figure 5: The value of $(2 \pi \sqrt{\alpha'})^4 e^{\mathcal{K}} |W|^2$ in units of $(\alpha')^2$ for vacua in the vicinity of $\psi = \phi = 0$, for $(2 \pi)^4 e^{\mathcal{K}} |W|^2 < 100000$. The flux range was (-20, 20), and the vacua satisfied the conditions (\ref{['solnconds']}).

Theorems & Definitions (1)

• Theorem 1: Yau