F-theory Grand Unified Theories Research Articles

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

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.

General gauge and anomaly mediated supersymmetry breaking in grand unified theories with vector-like particles

In Grand Unified Theories (GUTs) from orbifold and various string constructions the generic vector-like particles do not need to form complete SU(5) or SO(10) representations. To realize them concretely, we present orbifold SU(5) models, orbifold SO(10) models where the gauge symmetry can be broken down to flipped SU(5) X U(1)_X or Pati-Salam SU(4)_C X SU(2)_L X SU(2)_R gauge symmetries, and F-theory SU(5) models. Interestingly, these vector-like particles can be at the TeV-scale so that the lightest CP-even Higgs boson mass can be lifted, or play the messenger fields in the Gauge Mediated Supersymmetry Breaking (GMSB). Considering GMSB, ultraviolet insensitive Anomaly Mediated Supersymmetry Breaking (AMSB), and the deflected AMSB, we study the general gaugino mass relations and their indices, which are valid from the GUT scale to the electroweak scale at one loop, in the SU(5) models, the flipped SU(5) X U(1)_X models, and the Pati-Salam SU(4)_C X SU(2)_L X SU(2)_R models. In the deflected AMSB, we also define the new indices for the gaugino mass relations, and calculate them as well. Using these gaugino mass relations and their indices, we may probe the messenger fields at intermediate scale in the GMSB and deflected AMSB, determine the supersymmetry breaking mediation mechanisms, and distinguish the four-dimensional GUTs, orbifold GUTs, and F-theory GUTs.

Canonical gauge coupling unification in the standard model with high-scale supersymmetry breaking

Inspired by the string landscape and the unified gauge coupling relation in the F-theory Grand Unified Theories (GUTs) and GUTs with suitable high-dimensional operators, we study the canonical gauge coupling unification and Higgs boson mass in the Standard Model (SM) with high-scale supersymmetry breaking. In the SM with GUT-scale supersymmetry breaking, we achieve the gauge coupling unification at about 5.3 x 10^{13} GeV, and the Higgs boson mass is predicted to range from 130 GeV to 147 GeV. In the SM with supersymmetry breaking scale from 10^4 GeV to 5.3 x 10^{13} GeV, gauge coupling unification can always be realized and the corresponding GUT scale M_U is from 10^{16} GeV to 5.3 x 10^{13} GeV, respectively. Also, we obtain the Higgs boson mass from 114.4 GeV to 147 GeV. Moreover, the discrepancies among the SM gauge couplings at the GUT scale are less than about 4-6%. Furthermore, we present the SU(5) and SO(10) models from the F-theory model building and orbifold constructions, and show that we do not have the dimension-five and dimension-six proton decay problems even if M_U \le 5 x 10^{15} GeV.

Generalizing minimal supergravity

In Grand Unified Theories (GUTs), the Standard Model (SM) gauge couplings need not be unified at the GUT scale due to the high-dimensional operators. Considering gravity mediated supersymmetry breaking, we study for the first time the generic gauge coupling relations at the GUT scale, and the general gaugino mass relations which are valid from the GUT scale to the electroweak scale at one loop. We define the index k for these relations, which can be calculated in GUTs and can be determined at the Large Hadron Collider and the future International Linear Collider. Thus, we give a concrete definition of the GUT scale in these theories, and suggest a new way to test general GUTs at future experiments. We also discuss five special scenarios with interesting possibilities. With our generic formulae, we present all the GUT-scale gauge coupling relations and all the gaugino mass relations in the SU(5) and SO(10) models, and calculate the corresponding indices k. Especially, the index k is 5/3 in the traditional SU(5) and SO(10) models that have been studied extensively so far. Furthermore, we discuss the field theory realization of the U(1) flux effects on the SM gauge kinetic functions in F-theory GUTs, and calculate their indices k as well.

Particle Physics Implications of F-Theory

We review recent progress in realizing Grand Unified Theories (GUTs) in a strongly coupled formulation of type IIB string theory known as F-theory. This review's main emphasis is on the expected low-energy phenomenology of a minimal class of F-theory GUTs. We introduce the primary ingredients in such constructions, then present qualitative features of GUT models in this framework such as GUT breaking, doublet-triplet splitting, and proton decay. Next, we review proposals for realizing flavor hierarchies in the quark and lepton sectors. We discuss possible supersymmetry-breaking scenarios and their consequences for experiments, as well as geometrically minimal realizations of F-theory GUTs that incorporate most of these features.