Abstract
In F-theory GUTs, threshold corrections from Kaluza–Klein (KK) massive modes arising from gauge and matter multiplets play an important role in the determination of the weak mixing angle and the strong gauge coupling of the effective low energy model. In this Letter we further explore the induced modifications on the gauge couplings running and the GUT scale. In particular, we focus on the KK-contributions from matter curves and analyze the conditions on the chiral and Higgs matter spectrum which imply a GUT scale consistent with the minimal unification scenario. As an application, we present an explicit computation of these thresholds for matter fields residing on specific non-trivial Riemann surfaces.
Highlights
It is well known that the spectrum of the minimal supersymmetric extension of the Standard Model (SM) is consistent with a gauge couplings unification at a scale MGUT ∼ 2 × 1016 GeV
The SM gauge symmetry is embedded in the SU (5) Grand unified Theory (GUT) while the SM matter content is nicely assembled into SU (5) multiplets
In unified theories emerging in the context of F-theory compactification, threshold corrections from Kaluza-Klein massive modes play a decisive role in gauge coupling unification and the determination of the GUT scale
Summary
It is well known that the spectrum of the minimal supersymmetric extension of the Standard Model (SM) is consistent with a gauge couplings unification at a scale MGUT ∼ 2 × 1016 GeV. Threshold effects are generated at scales μ < MGUT when additional light degrees of freedom and in particular superpartners are integrated out The effects of the latter have been extensively studied in the context of supersymmetric and String Grand Unified Theories 2. In the present context of the SU (5) theory, these come along with massless gauge fields propagating in the bulk, while the chiral matter as well as the Higgs representations reside on two-dimensional Riemann surfaces (matter curves) Both kinds of KK-modes contribute to the gauge coupling running and can in principle modify the unification scale. We will proceed with an explicit calculation of the KK-massive modes thresholds originating from chiral and Higgs matter curves and show that their only net effect amounts to a shift of the common gauge coupling at the GUT scale.
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