Moduli stabilisation and the statistics of SUSY breaking in the landscape

Igor Broeckel,Kuver Sinha,Anshuman Maharana,Kajal Singh,Michele Cicoli

doi:10.1007/jhep10(2020)015

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 F- terms 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.

Highlights

It is important to understand if string theory can provide guidance in this regard
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
We will try to perform a systematic study of the interplay between Kahler moduli stabilisation and the statistics of the supersymmetry breaking scale by considering three general scenarios: (i) models with purely non-perturbative stabilisation like in KKLT vacua [30]; (ii) models where the Kahler moduli are frozen by balancing perturbative against non-perturbative effects as in the Large Volume Scenario (LVS) [31]; and (iii) models with purely perturbative stabilisation [32]

Summary

Introduction

It is important to understand if string theory can provide guidance in this regard. The literature on supersymmetry breaking and its mediation in string theory is vast, much of it focused on constructions of specific supersymmetry breaking and MSSM-like sectors (see [2,3,4,5,6] for a review of these and other aspects of string phenomenology). As described in [10], this program relies on several features of flux compactifications: they are the most wellunderstood string compactifications with moduli stabilisation and broken supersymmetry and provide a fertile arena where quantitative answers may be extracted; there are many vacua that at least roughly match the SM; the number of vacua is so large that statistical solutions make sense; and no single vacuum is favoured by the theory These studies found a preference for high scale supersymmetry due to a uniform distribution of the supersymmetry breaking scale [10, 13, 14]. Notice that these results match those derived in [10] since in these cases the F-terms of the Kahler moduli, to the dilaton and complex structure F-terms, turn out to be uniformly distributed

Objectives

Discussion

Conclusion