Jonathan J. Heckman

GUTs and Exceptional Branes in F-theory - II: Experimental Predictions

We consider realizations of GUT models in F-theory. Adopting a bottom up approach, the assumption that the dynamics of the GUT model can in principle decouple from Planck scale physics leads to a surprisingly predictive framework. An internal U(1) hypercharge flux Higgses the GUT group directly to the MSSM or to a flipped GUT model, a mechanism unavailable in heterotic models. This new ingredient automatically addresses a number of puzzles present in traditional GUT models. The internal U(1) hyperflux allows us to solve the doublet-triplet splitting problem, and explains the qualitative features of the distorted GUT mass relations for lighter generations due to the Aharanov-Bohm effect. These models typically come with nearly exact global symmetries which prevent bare ? terms and also forbid dangerous baryon number violating operators. Strong curvature around our brane leads to a repulsion mechanism for Landau wave functions for neutral fields. This leads to large hierarchies of the form exp(?c/?2?) where c and ? are order one parameters and ? ~ ?GUT?1MGUT/Mpl. This effect can simultaneously generate a viably small ? term as well as an acceptable Dirac neutrino mass on the order of 0.5 ? 10?2?0.5 eV. In another scenario, we find a modified seesaw mechanism which predicts that the light neutrinos have masses in the expected range while the Majorana mass term for the heavy neutrinos is ~ 3 ? 1012?1.5 GeV. Communicating supersymmetry breaking to the MSSM can be elegantly realized through gauge mediation. In one scenario, the same repulsion mechanism also leads to messenger masses which are naturally much lighter than the GUT scale.

On the Classification of 6D SCFTs and Generalized ADE Orbifolds

A bstractWe study (1, 0) and (2, 0) 6D superconformal field theories (SCFTs) that can be constructed in F-theory. Quite surprisingly, all of them involve an orbifold singularity ℂ2/Γ with Γ a discrete subgroup of U(2). When Γ is a subgroup of SU (2), all discrete subgroups are allowed, and this leads to the familiar ADE classification of (2, 0) SCFTs. For more general U(2) subgroups, the allowed possibilities for Γ are not arbitrary and are given by certain generalizations of the A- and D-series. These theories should be viewed as the minimal 6D SCFTs. We obtain all other SCFTs by bringing in a number of E-string theories and/or decorating curves in the base by non-minimal gauge algebras. In this way we obtain a vast number of new 6D SCFTs, and we conjecture that our construction provides a full list.

6d Conformal matter

A bstractA single M5-brane probing G, an ADE-type singularity, leads to a system which has G × G global symmetry and can be viewed as “bifundamental” (G, G) matter. For the AN series, this leads to the usual notion of bifundamental matter. For the other cases it corresponds to a strongly interacting (1, 0) superconformal system in six dimensions. Similarly, an ADE singularity intersecting the Hořava-Witten wall leads to a superconformal matter system with E8 × G global symmetry. Using the F-theory realization of these theories, we elucidate the Coulomb/tensor branch of (G, G′) conformal matter. This leads to the notion of fractionalization of an M5-brane on an ADE singularity as well as fractionalization of the intersection point of the ADE singularity with the Hořava-Witten wall. Partial Higgsing of these theories leads to new 6d SCFTs in the infrared, which we also characterize. This generalizes the class of (1, 0) theories which can be perturbatively realized by suspended branes in IIA string theory. By reducing on a circle, we arrive at novel duals for 5d affine quiver theories. Introducing many M5-branes leads to large N gravity duals.

Flavor Hierarchy From F-theory

Abstract It has recently been shown that F-theory based constructions provide a potentially promising avenue for engineering GUT models which descend to the MSSM. In this Note we show that in the presence of background fluxes, these models automatically achieve hierarchical Yukawa matrices in the quark and lepton sectors. At leading order, the existence of a U ( 1 ) symmetry which is related to phase rotations of the internal holomorphic coordinates at the brane intersection point leads to rank one Yukawa matrices. Subleading corrections to the internal wave functions from variations in the background fluxes generate small violations of this U ( 1 ) , leading to hierarchical Yukawa structures reminiscent of the Froggatt–Nielsen mechanism. The expansion parameter for this perturbation is in terms of α GUT . Moreover, we naturally obtain a hierarchical CKM matrix with V 12 ∼ V 21 ∼ e , V 23 ∼ V 32 ∼ e 2 , V 13 ∼ V 31 ∼ e 3 , where e ∼ α GUT , in excellent agreement with observation.

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 reviews 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.

T-branes and monodromy

We introduce T-branes, or “triangular branes”, which are novel non-abelian bound states of branes characterized by the condition that on some loci, their matrix of normal deformations, or Higgs field, is upper triangular. These configurations refine the notion of monodromic branes which have recently played a key role in F-theory phenomenology. We show how localized matter living on complex codimension one subspaces emerge, and explain how to compute their Yukawa couplings, which are localized in complex codimension two. Not only do T-branes clarify what is meant by brane monodromy, they also open up a vast array of new possibilities both for phenomenological constructions and for purely theoretical applications. We show that for a general T-brane, the eigenvalues of the Higgs field can fail to capture the spectrum of localized modes. In particular, this provides a method for evading some constraints on F-theory GUTs which have assumed that the spectral equation for the Higgs field completely determines a local model.

F-theory, GUTs, and the weak scale

In this paper we study a deformation of gauge mediated supersymmetry breaking in a class of local F-theory GUT models where the scale of supersymmetry breaking determines the value of the ? term. Geometrically correlating these two scales constrains the soft SUSY breaking parameters of the MSSM. In this scenario, the hidden SUSY breaking sector involves an anomalous U(1) Peccei-Quinn symmetry which forbids bare ? and B? terms. This sector typically breaks supersymmetry at the desired range of energy scales through a simple stringy hybrid of a Fayet and Polonyi model. A variant of the Giudice-Masiero mechanism generates the value ? ~ 102?103 GeV when the hidden sector scale of supersymmetry breaking is F1/2 ~ 108.5 GeV. Further, the B? problem is solved due to the mild hierarchy between the GUT scale and Planck scale. These models relate SUSY breaking with the QCD axion, and solve the strong CP problem through an axion with decay constant fa ~ MGUT??/?, where ? ~ 105 GeV is the characteristic scale of gaugino mass unification in gauge mediated models, and the ratio ?/? ~ MGUT/Mpl ~ 10?3. We find fa ~ 1012 GeV, which is near the high end of the phenomenologically viable window. Here, the axino is the goldstino mode which is eaten by the gravitino. The gravitino is the LSP with a mass of about 101?102 MeV, and a bino-like neutralino is (typically) the NLSP with mass of about 102?103 GeV. Compatibility with electroweak symmetry breaking also determines the value of tan? ~ 30?7.

The Point of E(8) in F-theory GUTs

We show that in F-theory GUTs, a natural explanation of flavor hierarchies in the quark and lepton sector requires a single point of E8 enhancement in the internal geometry, from which all Yukawa couplings originate. The monodromy group acting on the seven-brane configuration plays a key role in this analysis. Moreover, the E8 structure automatically leads to the existence of the additional fields and interactions needed for minimal gauge mediated supersymmetry breaking, and almost nothing else. Surprisingly, we find that in all but one Dirac neutrino scenario the messenger fields in the gauge mediated supersymmetry breaking sector transform as vector-like pairs in the

F-theory and Neutrinos: Kaluza-Klein Dilution of Flavor Hierarchy

10 \oplus \overline {10}

750 GeV Diphotons from a D3-brane

of SU(5). We also classify dark matter candidates available from this enhancement point, and rule out both annihilating and decaying dark matter scenarios as explanations for the recent experiments PAMELA, ATIC and FERMI. In F-theory GUT models, a 10–100 MeV mass gravitino remains as the prime candidate for dark matter, thus suggesting an astrophysical origin for recent experimental signals.