SUSY Breaking in Local String/F-Theory Models

TL;DR

The paper analyzes moduli stabilisation and SUSY breaking in local string/F-theory GUTs with the MSSM on del Pezzo surfaces or singularities, focusing on gravity mediation within the LARGE Volume Scenario. It shows that leading gravity- and anomaly-mediated contributions cancel, leaving highly suppressed soft terms that scale with the volume as $M_{3/2}/\sqrt{\mathcal{V}}$ (or smaller depending on uplift details), while the gravitino mass remains large ($M_{3/2}\sim M_P/\mathcal{V}$). This framework yields TeV-scale soft terms only for volumes $\mathcal{V}\sim 10^{6-7}$, making a GUT-scale unification consistent with a high string scale $M_s$, and opens the possibility of dominant gauge mediation under specific assumptions about the SUSY-breaking sector. The study also discusses implications for the cosmological moduli problem and outlines several phenomenological scenarios depending on uplift and α' corrections, highlighting the potential for heavy gravitino spectra and suppressed moduli-induced cosmological issues. Overall, it integrates LVS with local F-theory GUTs to derive computable, highly suppressed gravity-mediated soft terms and explores their cosmological and collider-scale consequences.

Abstract

We investigate bulk moduli stabilisation and supersymmetry breaking in local string/F-theory models where the Standard Model is supported on a del Pezzo surface or singularity. Computing the gravity mediated soft terms on the Standard Model brane induced by bulk supersymmetry breaking in the LARGE volume scenario, we explicitly find suppressions by M_s/M_P ~ V^{-1/2} compared to M_{3/2}. This gives rise to several phenomenological scenarios, depending on the strength of perturbative corrections to the effective action and the source of de Sitter lifting, in which the soft terms are suppressed by at least M_P/V^{3/2} and may be as small as M_P/V^2. Since the gravitino mass is of order M_{3/2} ~ M_P/V, for TeV soft terms all these scenarios give a very heavy gravitino (M_{3/2} >= 10^8 GeV) and generically the lightest moduli field is also heavy enough (m >= 10 TeV) to avoid the cosmological moduli problem. For TeV soft terms, these scenarios predict a minimal value of the volume to be V ~ 10^{6-7} in string units, which would give a unification scale of order M_{GUT} ~ M_s V^{1/6} ~ 10^{16} GeV. The strong suppression of gravity mediated soft terms could also possibly allow a scenario of dominant gauge mediation in the visible sector but with a very heavy gravitino M_{3/2} > 1 TeV.