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Gauge anomalous quantum field theories are inconsistent as full UV theories since they lead to the breaking of Lorentz invariance or Unitarity, as well as non-renormalizability. It is well known, however, that they can be interpreted as…
We consider a scenario in which the discrete weak symmetry between quarks and leptons is extended to the weak force by introducing exotic partners. We conjecture that there exists a hidden discrete symmetry $\tilde{P}$, defining a $Z_2$…
Inspired by a recently proposed GUT model based on the trinification ($\mathrm{SU}(3)^3$) gauge group with a global family ($\mathrm{SU}(3)_F$) symmetry, we consider an effective low-energy three Higgs doublet model that may shed light on…
The Standard Model has three generations of fermions and although it does not contain any explicit reason for this, the existence of additional generations is now very constrained by experiment. Present measurements are saturating…
The approach unifying all the internal degrees of freedom--proposed by one of us--is offering a new way of understanding families of quarks and leptons: A part of the starting Lagrange density in d(=1+13), which includes two kinds of spin…
Consider the addition of a right-handed SU(2) fermion multiplet (with neither color nor hypercharge) to each family of quarks and leptons. The resultant theory admits a new U(1) gauge symmetry only if the additional multiplet is a singlet…
Non-Abelian discrete family symmetries play a pivotal role in the formulation of models with tri-bimaximal lepton mixing. We discuss how to obtain symmetries such as A4, semidirect product of Z7 and Z3, and Delta(27) from an underlying…
In a supersymmetric SU(5) grand unified model with a horizontal symmetry SU(1,1), we discuss spontaneous generation of generations to produce three chiral generations of quarks and leptons and one generation of higgses by using one…
Flavour changing neutral currents arise in the $SU(3)_c\otimes SU(4)_L\otimes U(1)_X$ extension of the standard model because anomaly cancellation among the fermion families requires one generation of quarks to transform differently from…
Spectra, triple and quartic gauge couplings of the Higgsless model with gauge group $SU(2)_L\times SU(2)_R\times U(1)_{B-L}$ defined in warped space are explored with numerical method. We extend the equation of motions, boundary conditions…
We propose a supersymmetric extension of the anomaly-free and three families nonuniversal $U(1)$ model, with the inclusion of four Higgs doublets and four Higgs singlets. The quark sector is extended by adding three exotic quark singlets,…
The resonant excesses around 2 TeV reported by the ATLAS Collaboration can be explained in the left-right model, and the tight constraints from lepton plus missing energy searches can be evaded if the $SU(2)_R$ gauge symmetry is…
The structure of the quark and lepton masses and mixing angles provides one of the few windows we have on the underlying physics generating the \sm. In an attempt to identify the underlying symmetry group we look for the simplest gauge…
We propose the left-right models based on SU(3)_C\otimes SU(M)_L \otimes SU(N)_R \otimes U(1)_X gauge symmetry for (M,N)=(3,3), (2,3), and (3,2) that address the 750 GeV diphoton excess recently reported by the LHC. The fermion contents are…
Extending the well-known $SU(3)_C \times SU(3)_L \times SU(3)_R$ model of quarks and leptons to include a fourth $SU(3)_N$ gauge factor, a new realization is obtained, different from leptonic color, which contains a lepton/dark symmetry…
We investigate the quark-lepton symmetric gauge group in five dimensions, with the gauge symmetry broken by a combination of orbifold compactification of the extra dimension and the Higgs mechanism. The gauge sector of the model is…
We present supersymmetric, tadpole-free d=4,N=1 orientifold vacua with a three family chiral fermion spectrum that is identical to that of the Standard Model. Starting with all simple current orientifolds of all Gepner models we perform a…
A considerable amount of the standard model's three-generation structure can be realised from just the $8\hspace{.3mm}\mathbb{C}$-dimensional algebra of the complex octonions. Indeed, it is a little-known fact that the complex octonions can…
We investigate the neutrino masses and mixing patten in a version of the $SU(3)_c\otimes SU(3)_L\otimes U(1)_X$ model with one extra exotic charged lepton per family as introduced by Ozer. It is shown that an extended scalar sector,…
We present new techniques for finding anomaly-free sets of fermions. Although the anomaly cancellation conditions typically include cubic equations with integer variables that cannot be solved in general, we prove by construction that any…