Scanning the Landscape of Flux Compactifications: Vacuum Structure and Soft Supersymmetry Breaking

TL;DR

This work analyzes the vacuum structure of flux compactifications on the Calabi-Yau $\mathbb{P}^4_{[1,1,1,6,9]}$ by scanning the flux superpotential value $W_0$ over many orders of magnitude to map AdS and dS vacua. Using an effective $\mathcal{N}=1$ supergravity framework with $\hat{W}=W_0+\sum_i A_i e^{-a_i T_i}$ and a two-moduli Kähler potential, the authors identify regimes resembling KKLT and LVS and uncover a new deeper non-supersymmetric minimum. They derive how the bare cosmological constant and soft supersymmetry-breaking terms on D7-branes depend on $W_0$ across these minima, including analytic insights for SUSY conditions and the behavior of the volume $\mathcal{V}$ as $W_0\to 0$. The results illuminate how different flux choices sculpt the low-energy physics and have potential applications in phenomenology and model-building within Type IIB flux vacua.

Abstract

We scan the landscape of flux compactifications for the Calabi-Yau manifold $\mathbb{P}^4_{[1,1,1,6,9]}$ with two K\" ahler moduli by varying the value of the flux superpotential $W_0$ over a large range of values. We do not include uplift terms. We find a rich phase structure of AdS and dS vacua. Starting with $W_0\sim 1$ we reproduce the exponentially large volume scenario, but as $W_0$ is reduced new classes of minima appear. One of them corresponds to the supersymmetric KKLT vacuum while the other is a new, deeper non-supersymmetric minimum. We study how the bare cosmological constant and the soft supersymmetry breaking parameters for matter on D7 branes depend on $W_0$, for these classes of minima. We discuss potential applications of our results.