non-Abelian Discrete Gauge Symmetries Research Articles

Type II string theory on Calabi-Yau manifolds with torsion and non-Abelian discrete gauge symmetries

We provide the first explicit example of Type IIB string theory compactification on a globally defined Calabi-Yau threefold with torsion which results in a four-dimensional effective theory with a non-Abelian discrete gauge symmetry. Our example is based on a particular Calabi-Yau manifold, the quotient of a product of three elliptic curves by a fixed point free action of {mathbb{Z}}_2times {mathbb{Z}}_2 . Its cohomology contains torsion classes in various degrees. The main technical novelty is in determining the multiplicative structure of the (torsion part of) the cohomology ring, and in particular showing that the cup product of second cohomology torsion elements goes non-trivially to the fourth cohomology. This specifies a non-Abelian, Heisenberg-type discrete symmetry group of the cfour-dimensional theory.

Non-Abelian discrete gauge symmetries in F-theory

The presence of non-Abelian discrete gauge symmetries in four-dimensional F-theory compactifications is investigated. Such symmetries are shown to arise from seven-brane configurations in genuine F-theory settings without a weak string coupling description. Gauge fields on mutually non-local seven-branes are argued to gauge both R-R and NS-NS two-form bulk axions. The gauging is completed into a generalisation of the Heisenberg group with either additional seven-brane gauge fields or R-R bulk gauge fields. The former case relies on having seven-brane fluxes, while the latter case requires torsion cohomology and is analysed in detail through the M-theory dual. Remarkably, the M-theory reduction yields an Abelian theory that becomes non-Abelian when translated into the correct duality frame to perform the F-theory limit. The reduction shows that the gauge coupling function depends on the gauged scalars and transforms non-trivially as required for the groups encountered. This field dependence agrees with the expectations for the kinetic mixing of seven-branes and is unchanged if the gaugings are absent.

Non-Abelian discrete gauge symmetries in 4d string models

We study the realization of non-Abelian discrete gauge symmetries in 4d field theory and string theory compactifications. The underlying structure generalizes the Abelian case, and follows from the interplay between gaugings of non-Abelian isometries of the scalar manifold and field identifications making axion-like fields periodic. We present several classes of string constructions realizing non-Abelian discrete gauge symmetries. In particular, compactifications with torsion homology classes, where non-Abelianity arises microscopically from the Hanany-Witten effect, or compactifications with non-Abelian discrete isometry groups, like twisted tori. We finally focus on the more interesting case of magnetized branes in toroidal compactifications and quotients thereof (and their heterotic and intersecting duals), in which the non-Abelian discrete gauge symmetries imply powerful selection rules for Yukawa couplings of charged matter fields. In particular, in MSSM-like models they correspond to discrete flavour symmetries constraining the quark and lepton mass matrices, as we show in specific examples.

Inflationary models with a flat potential enforced by non-Abelian discrete gauge symmetries

Non-abelian discrete gauge symmetries can provide the inflaton with a flat potential even when one takes into account gravitational strength effects. The discreteness of the symmetries also provide special field values where inflation can end via a hybrid type mechanism. An interesting feature of this method is that it can naturally lead to extremely flat potentials and so, in principle, to inflation at unusually low energy scales. Two examples of effective field theories with this mechanism are given, one with a hybrid exit and one with a mutated hybrid exit. They include an explicit example in which the single field consistency condition is violated.

Non-abelian discrete gauge symmetries and inflation

Obtaining a potential flat enough to provide slow roll inflation is often difficult when gravitational effects are included. Non-abelian discrete gauge symmetries can guarantee the flatness of the inflaton potential in this case, and also provide special field values where inflation can end.

Hexagonal theory of flavor

We construct a supersymmetric theory of flavor based on the discrete gauge group (D_6)^2, where D_6 describes the symmetry of a regular hexagon under proper rotations in three dimensions. The representation structure of the group allows one to distinguish the third from the lighter two generations of matter fields, so that in the symmetry limit only the top quark Yukawa coupling is allowed and scalar superpartners of the first two generations are degenerate. Light fermion Yukawa couplings arise from a sequential breaking of the flavor symmetry, and supersymmetric flavor-changing processes remain adequately suppressed. We contrast our model with others based on non-Abelian discrete gauge symmetries described in the literature, and discuss the challenges in constructing more minimal flavor models based on this approach.

Flavor “conservation” and hierarchy in TeV-scale supersymmetric standard model

Recently a TeV-scale Supersymmetric Standard Model (TSSM) was proposed in which the gauge coupling unification is as precise (at one loop) as in the MSSM, and occurs in the TeV range. Proton stability in the TSSM is due to an anomaly free z 3 ⊗ z 3 discrete gauge symmetry, which is also essential for successfully generating neutrino masses in the desirable range. In this paper we show that the TSSM admits anomaly free non-Abelian discrete flavor gauge symmetries (based on a left-right product tetrahedral group) which together with a “vector-like” Abelian (discrete) flavor gauge symmetry suppresses dangerous higher dimensional operators corresponding to flavor changing neutral currents (FCNCs) to an acceptable level. Discrete flavor gauge symmetries are more advantageous compared with continuous flavor gauge symmetries as the latter must be broken, which generically results in unacceptably large gauge mediated flavor violation. In contrast, in the case of discrete flavor gauge symmetries the only possibly dangerous sources of flavor violation either come from the corresponding “bulk” flavon (that is, flavor symmetry breaking Higgs) exchanges, or are induced by flavon VEVs. These sources of flavor violation, however, are adequately suppressed by the above flavor gauge symmetries for the string scale ∼ 10–100 TeV.