Abelian Discrete Symmetries Research Articles

Classification of Abelian domain walls

We discuss domain walls from spontaneous breaking of Abelian discrete symmetries $Z_N$. A series of different domain wall structures are predicted, depending on the symmetry and charge assignments of scalars leading to the spontaneous symmetry breaking (SSB). A widely-existing type of domain walls are those separating degenerate vacua which are adjacent in the field space. We denote these walls as adjacency walls. In the case that $Z_N$ terms are small compared with the $U(1)$ terms, the SSB of $U(1)$ generates strings first and then adjacency walls bounded by strings are generated after the SSB of $Z_N$. For symmetries larger than $Z_3$, non-adjacent vacua exist, we regard walls separating them as non-adjacency walls. These walls are unstable if $U(1)$ is a good approximation. If the discrete symmetry is broken via multiple steps, we arrive at a complex structure that one kind of walls wrapped by another type. On the other hand, if the symmetry is broken in different directions independently, walls generated from the different breaking chains are blind to each other.

Seesaw mechanism in the R-parity-violating supersymmetric standard model with the gauged flavor U(1)X symmetry

Abstract We study the seesaw mechanism in the supersymmetric standard model (SSM) with the ${\mathbb {Z}}_3$ symmetry called matter triality (M3). The Abelian discrete symmetry prohibits the baryon number violation operators at the (non-)renormalizable level, which ensures proton longevity. The cubic coupling by right-handed neutrinos generates the Majorana mass term after the right-handed sneutrinos develop into the vacuum expectation values. Due to the R-parity violation, the active neutrino masses can be generated not only from the mixings with the right-handed neutrinos but also from those with the minimal SSM neutralinos. We propose a model where M3 is embedded in the gauged flavor symmetry. The flavor charges are constrained by the anomaly cancellation conditions and the requirements to realize the fermion masses and mixing angles in the quark and lepton sectors. We analyze the assignments of the flavor charge, and show that the sterile neutrino mass is allowed to be below the soft supersymmetry-breaking scale, which is constrained by the half-lifetime of the neutrinoless double beta decay.

Dynamical symmetry breaking and fermion mass hierarchy in the scale-invariant 3-3-1 model

We propose an extension of the Standard Model (SM) based on the $SU(3)_C\otimes SU(3)_L\otimes U(1)_X$ (3-3-1) gauge symmetry and scale invariance. Maintaining the main features of the so-called 3-3-1 models, such as the cancellation of gauge anomalies related to the number of chiral fermion generations, this model exhibits a very compact scalar sector. Only two scalar triplets and one singlet are necessary and sufficient to break the symmetries dynamically via the Coleman-Weinberg mechanism. With the introduction of an Abelian discrete symmetry and assuming a natural hierarchy among the vacuum expectation values of the neutral scalar fields, we show that all particles in the model can get phenomenologically consistent masses. In particular, most of the standard fermion masses are generated via a seesaw mechanism involving some extra heavy fermions introduced for consistency. This mechanism provides a partial solution for the fermion mass hierarchy problem in the SM. Furthermore, the simplicity of the scalar sector allows us to analytically find the conditions for the potential stability up to one-loop level and show how they can be easily satisfied. Some of the new particles, such as the scalars $H$, $H^\pm$ and all the non-SM vector bosons, are predicted to get masses around the TeV scale and, therefore, could be produced at the high-luminosity LHC. Finally, we show that the model features a residual symmetry which leads to the stability of a heavy neutral particle; the latter is expected to show up in experiments as missing energy.

Supersymmetric M2-branes with Englert fluxes, and the simple group PSL(2, 7)

A new class is introduced of M2-branes solutions of d=11 supergravity that include internal fluxes obeying Englert equation in 7-dimensions. A simple criterion for the existence of Killing spinors in such backgrounds is established. Englert equation is viewed as the generalization to d=7 of Beltrami equation defined in d=3 and it is trated accordingly. All 2-brane solutions of minimal d=7 supergracity can be uplifted to d=11 and have N > 4 or N = 4 supersymmetry. It is shown that the simple group PSL(2,7) is crystallographic in d=7 having an integral action on the A7 root lattice. By means of this point-group and of the T7 torus obtained quotiening R7 with the A7 root lattice we were able to construct new M2 branes with Englert fluxes and N < 4. In particular we exhibit here an N=1 solution depending on 4-parameters and admitting a large non abelian discrete symmetry, namely G21 = Z3 semidirect product with Z7 = subgroup of PSL(2,7). The dual d=3 field theories have the same symmetries and have complicated non linear interactions.

Discrete symmetries from hidden sectors

We study the presence of abelian discrete symmetries in globally consistent orientifold compactifications based on rational conformal field theory. We extend previous work [1] by allowing the discrete symmetries to be a linear combination of U(1) gauge factors of the visible as well as the hidden sector. This more general ansatz significantly increases the probability of finding a discrete symmetry in the low energy effective action. Applied to globally consistent MSSM-like Gepner constructions we find multiple models that allow for matter parity or Baryon triality.

Abelian discrete symmetries [formula omitted] and [formula omitted] from string orbifolds

We show that Abelian discrete symmetries ZN and ZnR from string orbifolds result by assigning vacuum expectation values (VEVs) only to specified singlets. These singlets obtaining VEVs carry the gauge charges (of the covering U(1) gauge group) as multiples of N for ZN and n for ZnR. We explicitly show this realization in a Z12−I orbifold model.

Froggatt-Nielsen model for leptophilic scalar dark matter decay

We construct a model of decaying, TeV-scale scalar dark matter motivated by data from the PAMELA and Fermi-LAT experiments. By introducing an appropriate Abelian discrete symmetry and an intermediate scale of vector-like states that are responsible for generating lepton Yukawa couplings, we show that Planck-suppressed corrections may lead to decaying dark matter that is leptophilic and has the desired lifetime. The dark matter candidate decays primarily to lepton/anti-lepton pairs, and at a subleading rate to final states with a lepton, anti-lepton and standard model Higgs boson. We show that the model can reproduce the observed positron flux and positron fraction while remaining consistent with the bounds on the cosmic ray antiproton flux.

A unique [formula omitted] symmetry for the MSSM

We consider the possible anomaly free Abelian discrete symmetries of the MSSM that forbid the μ-term at perturbative order. Allowing for anomaly cancellation via the Green–Schwarz mechanism we identify discrete R-symmetries as the only possibility and prove that there is a unique Z4R symmetry that commutes with SO(10). We argue that non-perturbative effects will generate a μ-term of electroweak order thus solving the μ-problem. The non-perturbative effects break the Z4R symmetry leaving an exact Z2 matter parity. As a result dimension four baryon- and lepton-number violating operators are absent while, at the non-perturbative level, dimension five baryon- and lepton-number violating operators get induced but are highly suppressed so that the nucleon decay rate is well within present bounds.

Majorana mass zeros from Higgs triplet vacuum expectation values without a Majoron problem

It is shown how to obtain recently-proposed two-zero Majorana mass textures in models with three Higgs triplets with small VEVs and a sufficiently massive triplet Majoron by using abelian discrete symmetries. It is briefly discussed how in SU(5) grand unification where the triplets occur in {\bf 15}'s the neutrino textures can be related to up- and down- quark mass textures.

Limit theorems for spin systems with an Abelian discrete symmetry

Exponential convergence in the number of states is proved for the pressure of a class of discrete Abelian spin systems, to the O(2) invariant model’s pressure in d dimensions. Analogous results are obtained for the convergence of the expectation values of a class of functions under more stringent conditions.