Moduli Stabilisation and the Statistics of SUSY Breaking in the Landscape

TL;DR

This paper investigates how including K"ahler moduli stabilisation affects the distribution of supersymmetry breaking scales in the string landscape, revealing different patterns for KKLT and LVS vacua.

Contribution

It systematically incorporates K"ahler moduli into landscape statistics, showing their crucial role in determining the distribution of SUSY breaking scales.

Findings

KKLT vacua favor high-scale supersymmetry with power-law distribution.

LVS vacua favor low-scale supersymmetry with logarithmic distribution.

The overall landscape distribution depends on the prevalence of LVS versus KKLT vacua.

Abstract

The statistics of the supersymmetry breaking scale in the string landscape has been extensively studied in the past finding either a power-law behaviour induced by uniform distributions of F-terms or a logarithmic distribution motivated by dynamical supersymmetry breaking. These studies focused mainly on type IIB flux compactifications but did not systematically incorporate the K\"ahler moduli. In this paper we point out that the inclusion of the K\"ahler moduli is crucial to understand the distribution of the supersymmetry breaking scale in the landscape since in general one obtains unstable vacua when the F-terms of the dilaton and the complex structure moduli are larger than the F-terms of the K\"ahler moduli. After taking K\"ahler moduli stabilisation into account, we find that the distribution of the gravitino mass and the soft terms is power-law only in KKLT and perturbatively stabilised vacua which therefore favour high scale supersymmetry. On the other hand, LVS vacua feature a logarithmic distribution of soft terms and thus a preference for lower scales of supersymmetry breaking. Whether the landscape of type IIB flux vacua predicts a logarithmic or power-law distribution of the supersymmetry breaking scale thus depends on the relative preponderance of LVS and KKLT vacua.