Moduli Stabilisation and the Statistics of SUSY Breaking in the Landscape

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 Kähler moduli. In this paper we point out that the inclusion of the Kähler 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 Fterms of the Kähler moduli. After taking Kähler 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.

Superheavy Dark Matter from String Theory

“…This solution therefore is not very generic. We note that statistical studies showed that high scale supersymmetry is a generic feature of the string landscape regardless of inflation [18,19].…”

“…In this paper we have argued that two generic features of string compactifications, a high supersymmetry breaking scale (which is favored by both statistical arguments [18,19] and by the requirement of a viable inflationary model building [15]) and the presence of light moduli which drive epochs of EMD [7][8][9], lead typically to superheavy WIMP DM with mass around the intermediate scale. This scenario has not received significant attention so far because DM with a mass in the 10 10 -10 11 GeV range is inevitably overproduced in a standard thermal history.…”

Supersymmetry and R-symmetries in Wess-Zumino models: properties and model dataset construction

“…The metastable SUSY breaking model ( 126) is an example of this case. If (146) can not be solved, one needs to minimize part of the scalar potential from R-charge 0 F-terms:…”

Lectures on Naturalness, String Landscape and Multiverse

“…As emphasised e.g. very recently in[341], the Kahler moduli stabilisation is also crucial. However, at that level of detail one must also consider the statistics of possible uplifts -a hard subject that is not well understood.…”