Branches of the Landscape

TL;DR

This work analyzes the flux landscape by classifying vacua into three branches determined by tree-level SUSY breaking and $W$-value: branch one with broken SUSY at the fundamental scale, branch two with unbroken SUSY and $W\neq 0$, and branch three with unbroken SUSY and $W=0$. It shows that branch one features an infinite, largely intractable set of non-supersymmetric stationary points, while the $\ abla$-expansion imposes a cutoff and makes counting meaningful only at small SUSY breaking scales; the density of states scales as $\Lambda_0 F^{*6}$ under reasonable assumptions, and moduli stabilization via KKLT-like mechanisms can fix Kahler moduli in some vacua with small SUSY breaking, though most such states are short-lived. Branch two appears computable and potentially predictive, with KKLT-like AdS vacua and possible correlations between small $\langle W \rangle$ and small cosmological constant; branch three centers on discrete R-symmetries leading to $W=0$ vacua, which may have favorable phenomenological features but come with a substantial suppression from flux-space reductions. Overall, the paper argues that while branch one remains hard to constrain, branches two and three offer concrete avenues for predictions about the scale and pattern of supersymmetry breaking, contingent on further statistical data for gauge groups, matter content, and discrete symmetries. The conclusions emphasize that naturalness in the landscape may still align with low-energy SUSY on computable branches, though decisive predictions require deeper statistical understanding of vacua distributions.

Abstract

With respect to the question of supersymmetry breaking, there are three branches of the flux landscape. On one of these, if one requires small cosmological constant, supersymmetry breaking is predominantly at the fundamental scale; on another, the distribution is roughly flat on a logarithmic scale; on the third, the preponderance of vacua are at very low scale. A priori, as we will explain, one can say little about the first branch. The vast majority of these states are not accessible even to crude, approximate analysis. On the other two branches one can hope to do better. But as a result of the lack of access to branch one, and our poor understanding of cosmology, we can at best conjecture about whether string theory predicts low energy supersymmetry or not. If we hypothesize that are on branch two or three, distinctive predictions may be possible. We comment of the status of naturalness within the landscape, deriving, for example, the statistics of the first branch from simple effective field theory reasoning.