Gauge coupling unification in E 6 F-theory GUTs with matter and bulk exotics from flux breaking

Abstract

We consider gauge coupling unification in E 6 F-Theory Grand Unified Theories (GUTs) where E 6 is broken to the Standard Model (SM) gauge group using fluxes. In such models there are two types of exotics that can affect gauge coupling unification, namely matter exotics from the matter curves in the 27 dimensional representation of E 6 and the bulk exotics from the adjoint 78 dimensional representation of E 6. We explore the conditions required for either the complete or partial removal of bulk exotics from the low energy spectrum. In the latter case we shall show that (miraculously) gauge coupling unification may be possible even if there are bulk exotics at the TeV scale. Indeed in some cases it is necessary for bulk exotics to survive to the TeV scale in order to cancel the effects coming from other TeV scale matter exotics which would by themselves spoil gauge coupling unification. The combination of matter and bulk exotics in these cases can lead to precise gauge coupling unification which would not be possible with either type of exotics considered by themselves. The combination of matter and bulk exotics at the TeV scale represents a unique and striking signature of E 6 F-theory GUTs that can be tested at the LHC.