Zero textures of the neutrino mass matrix from cyclic family symmetry

We present the symmetry realization of the phenomenologically viable Frampton-Glashow-Marfatia (FGM) two zero texture neutrino mass matrices in the flavor basis within the framework of the type (I+II) seesaw mechanism natural to SO(10) grand unification. A small Abelian cyclic symmetry group Z₃ is used to realize these textures except for class C for which the symmetry is enlarged to Z₄. The scalar sector is restricted to the Standard Model (SM) Higgs doublet to suppress the flavor changing neutral currents. Other scalar fields used for symmetry realization are at the most two scalar triplets and, in some cases, a complex scalar singlet. Symmetry realization of one zero textures has, also, been presented.     

Breaking of the SO(n) symmetry with vector and adjoint higgses

The spontaneous symmetry breaking of SO(n) is investigated by studying the most general quartic SO(n)-invariant Higgs potential with two multiplets of scalars belonging to a vector and to an adjoint representation. In the most general cases largest residual symmetry is found to be SU(l), SU(l-1), SO(l), SO(l-1) or SO(n-2) wherel is the rank of SO(n). In particular, the breaking of SO(n) into SU(n ₁)×SU(n ₂) is found to occur only in special cases.     

Prospects for supersymmetric SO(10) models with an intermediate mass scale

We investigate possible patterns of SO(10) gauge symmetry breaking compatible with supersymmetry, limiting ourselves to the cases with one intermediate breaking scale. It is found that the one where a 54 representation breaks SO(10) into a Pati-Salam group SU(4)_C×SU(2)_L×SU(2)_R and the one where a 210 breaks it into SU(3)_C× U(1)_C×SU(2)_L×SU(2)_R are the most preferable patterns when supersymmetry is taken into account. Two models with the Pati-Salam intermediate symmetry are studied in more detail.     

Chiral fermion generations from higher-dimensional gravity

We discuss a six-dimensional SO(12) gauge theory which can be obtained from pure gravity in 18 dimensions coupled to a Majorana-Weyl spinor, if the ground state is characterized by a noncompact internal space without boundary with small finite volume. The six-dimensional SO(12) theory spontaneously compactifies to a four-dimensional SO(10) theory with local generation group SU(2)_G × U(1)_G. We obtain an even number of chiral fermion generations transforming as ($\text{16, k, ±}\text{1}\text{2}$) under SO(10) × SU(2)_G × U(1)_G. Adding a scalar field to the six-dimensional theory provides us with fields carrying all the quantum numbers needed for a realistic spontaneous symmetry breakdown to SU(3)_c × U(1)_e.m.     

N = 4 supergravity coupled to N = 4 matter and hidden symmetries

We present the N = 1 supergravity in 10 dimensions obtained by truncating the reduced N = 1 supergravity from 11 dimensions. This is further reduced to 4 dimensions to give SU(4) supergravity coupled to six SO(4) vector multiplets. As the reduction is from 10 dimensions, the theory is expected to have the symmetry SL(6R)_global×SO(6)_local, but we give a theoretical argument that this can be extended to SO(6,6)×SU(1,1)_global and SO(6)×SO(6)×U(1)_local.     

On the use of the group SO(4, 2) in atomic and molecular physics

The dynamical non-invariance group SO(4, 2) for a hydrogen-like atom is derived through two different approaches. The first one is by an established traditional ascent process starting from the symmetry group SO(3). This approach is presented in a mathematically oriented original way with a special emphasis on maximally superintegrable systems, N-dimensional extension and little groups. The second approach is by a new symmetry descent process starting from the non-invariance dynamical group Sp(8, R) for a four-dimensional harmonic oscillator. It is based on the little known concept of a Lie algebra under constraints and corresponds in some sense to a symmetry breaking mechanism. This paper ends with a brief discussion of the interest of SO(4, 2) for a new group-theoretical approach to the periodic table of chemical elements. In this connection, a general ongoing programme based on the use of a complete set of commuting operators is briefly described. It is believed that the present paper could be useful not only to the atomic and molecular community but also to people working in theoretical and mathematical physics.     

Spontaneous symmetry breaking and fermion chirality in higher-dimensional gauge theory

The number of chiral fermions may change in the course of spontaneous symmetry breaking. We discuss solutions of a six-dimensional Einstein-Yang-Mills theory based on SO(12). In the resulting effective four-dimensional theory they can be interpreted as spontaneous breaking of a gauge group SO(10) to $\text{H}\text{=}\text{SU}\text{(3)}{}_{\mathrm{<mtext>C</mtext>}}\text{×}\text{SU}\text{(2)}{}_{\mathrm{<mtext>L</mtext>}}\text{×}\text{U}\text{(1)}{}_{\mathrm{<mtext>R</mtext>}}\text{×}\text{U}\text{(10)}{}_{\mathrm{B?L}}$. For all solutions, the fermions which are chiral with respect to $\text{H}$ form standard generations. However, the number of generations for the solutions with broken SO(10) may be different compared to the symmetric solutions. All solutions considered here exhibit a local generation group SU(2)_G × U(1)_G. For the solutions with broken SO(10) symmetry, the leptons and quarks within one generation transform differently with respect to SU(2)_G × U(1)_G. Spontaneous symmetry breaking also modifies the SO(10) relations among Yukawa couplings. All this has important consequences for possible fermion mass relations obtained from higher-dimensional theories.     

Negative dimensions and E7 symmetry

The invariant length and volume which characterize the Lorentz group are extended to a quadratic and a quartic supersymmetric invariant. The symmetry group of the Grassmann sector can be SO(2), SU(2), SU(2) × SU(2) × SU(2), Sp(6), SU(6), SO(12) or E₇, which are also possible global symmetries of extended supergravities. Diophantine conditions which yield this classification follow from the corresponding conditions in d bosonic dimensions by the replacement d → ?d.     

Representations ofSO(p+q) andO(p) with an application to the shapes of8,9Li

It is easy to show that the symmetry groups governing a system ofZ protons andN neutrons areSO(p+q) andO(p), wherep, q are related toZ, N and the symmetry groups are transitive on a Grassmann manifoldG _p,q. In this paper the general representations ofSO(p+q) andO(p) are found and used to describe the geodesics onG _p,q for the nuclear manifolds of the neutron rich-elements^8,9Li.     

Morphology of InN nanorods using spectroscopic Raman imaging

We report the vibrational properties of vertical and oblique InN nanorods (NRs) grown by molecular beam epitaxy (MBE). Surface optical (SO) Raman mode at 561 cm⁻¹, belonging to E₁ symmetry [SO(E₁)], is identified along with symmetry allowed Raman modes of E₂(low), E₂(high), and E₁(LO) at 87, 489, and 589 cm⁻¹, respectively, corresponding to wurtzite InN phase. Usually, SO phonon modes arise due to breakdown of translational symmetry of surface potential at surface defects, which are attributed by the surface roughness. Intensity distribution of E₁(LO) and SO(E₁) phonon modes over a specified area have been analysed using Raman area mapping with an optical resolution of 400 nm. Imaging with E₁(LO) phonon mode, originating from the bulk of the sample, distinguishes the vertical NRs alone. We are able to resolve NR morphologies in both vertical and oblique cases with additional Raman mapping analysis of SO(E₁) phonon mode, emerging from the surface irregularities, which are confined to the tip of MBE grown NRs. Copyright © 2013 John Wiley & Sons, Ltd.     

Spin-spin and spin-other-orbit effects of optical spectra and the spin-Hamiltonian parameters for Cr ions in MgO crystals

An extended complete diagonalization method/microscopic spin-Hamiltonian (CDM/MSH) program has been developed, which is applicable for d³ ions at sites of tetragonal symmetry type I (C_4v, D_2d, D₄, D_4h) and trigonal symmetry type I (C_3v, D₃, D_3d). The Hamiltonian includes the spin-spin (SS) and spin-other-orbit (SOO) magnetic interactions besides the spin-orbit (SO) magnetic interaction usually taken into account. Utilizing the extended CDM/MSH program, the optical spectra, the spin-Hamiltonian (SH) parameters of the ground state ⁴B₁, and the splitting δ(²E) of the first excited ²E state for Cr³⁺ (3d³) ions at C_4v symmetry sites in MgO crystals have been successfully investigated. It is found that although the SO magnetic interaction is the most important one, the contributions to the SH parameters and the optical spectra from the SS and SOO magnetic interactions for Cr³⁺:MgO crystals are appreciable and should not be omitted, especially reaching 27.8% for the zero field splitting parameter D.     

Holographic multi-band superconductor

We propose a gravity dual for the holographic superconductor with multi-band carriers. Moreover, the currents of these carriers are unified under a global flavored SO(3) symmetry, which is dual to the bulk SO(3) gauge symmetry. We study the phase diagram of our model, and find it qualitatively agrees with the one for the realistic 2-band superconductor, such as MgB₂. We also identify the bulk field dual to the electromagnetic UEM(1) current, which should be invariant under the global flavored SO(3) rotation. We then evaluate the corresponding holographic conductivity and find the expected mean field like behaviors.     

Vibronic coupling effects in the C60 molecule

Many recent experiments have established that the Jahn-Teller (JT) effect plays a very important role in determining the properties of the C₆₀ molecule. A review of the underlying theory developed by the Nottingham group is presented for cases in which distinct minima in the potential energy surface occur. This relates directly to the C₆₀ molecule through the consideration of the T ⊗ h and H ⊗ h JT systems. When only linear coupling terms exist in the T ⊗ h system, the minima form a continuous trough of SO(3) symmetry and new methods must be used. Some details of these results are presented.     

On the phenomenological group in the unified SO(10) model

We analyze possible low energy effects of the additional U(1) contained in the symmetry breaking chain: SO(10)→SU(5) ? U(1) →…, stressing the importance of considering extensions of SU(2) ? U(1) as subgroups of grand unified models, in order to use the relations between the coupling constants provided by the renormalization group. We also investigate the possibility of employing this extra U(1) for an explanation of the possible discrepancy between the experimental value of sin²θ_w and its renormalized value in the SU(5) model.     

A unified treatment of the groups SO(4) and SO(3,1)

The irreducible representations of the group SO(4) in which the SO(3) subgroup is reduced are studied by an explicit construction of the operators and the basis in the spinor representation. The basis function which is formally identical with that for the coupling of two angular momentaj ₁ andj ₂ is expressible in terms of a hypergeometric function and strongly resembles the one for the irreducible representations of the groups SO(3,1). For the Lorentz group, the bases for the unitary representations which require unphysical values ofj ₁ andj ₂ are found to be analytic continuation of those for SO(4). The realization of the unitary irreducible representations of the group SO(4) in the Hilbert space of these functions leads, for appropriate unphysical values ofj ₁,j ₂, to the Gelfand-Naimark formula for the principal and complementary series of the representations of SO(3;1). The matrix elements for finite transformations of SO(4) and SO(3,1) can be evaluated, in this approach, in a unified manner by using standard properties of the hypergeometric function. These turn out to be a finite sum of₃ F ₂-functions which, as expected, are polynomials for SO(4) and infinite series for SO(3,1). A number of special matrix elements are calculated from the general formula and these agree with the results obtained previously.The authors are deeply indebted to Professor S.Dutta Majumdar fo many important suggestions and clarifications.     

Implications of a natural fermion mass hierarchy

The hierarchical struture of the fundamental fermion mass spectra is required to arise in a non-accidental way from a unified model G_family with a horizontal symmetry factor group G_generation. A quark or lepton must then not be in the same representation of G_family as its anti-particle. Models for G_family of the type SU(4)_C × SU(2)_L × SU(2)_R are favoured over SU(5) or SO(10).     

Phase transitions and magnetic monopoles in SO(10)

In a unified gauge theory based on SO(10), the combination of a strongly first order phase transition and a magnetic confinement mechanism can suppress the density of magnetic monopoles at the time of nucleosynthesis. However, this only occurs if SO(10) breaks down to SU(3)_c ? U (1)_em via SU(4)_c ? [SU(2)_L × SU(2)_R]. For the other symmetry breaking patterns of SO(10) obtained with a minimal Higgs system, the potential conflict with the standard big bang cosmology is not naturally avoided.     

Higgs–matter splitting in quasi-realistic orbifold string GUTs

E₆ grand unification combines the standard model matter and Higgs states in the single 27 representation. I discuss how the E₆ structure underlies the quasi-realistic free fermion heterotic-string models. E₆→SO(10)×U(1) breaking is obtained by a GSO phase in the N=1 partition function. The equivalence of this symmetry breaking phase with a particular choice of boundary condition basis vectors, which is used in the quasi-realistic models, is demonstrated in several cases. As a result, matter states in the spinorial 16 representation of SO(10) arise from the twisted sectors, whereas the Higgs states arise from the untwisted sector. Possible additional phenomenological implications of this E₆ symmetry breaking pattern are discussed.     

On the SO(7) symmetry of the SO(8) monopole and quadrupole pairing model

The SO(7) D-pairing symmetry of the SO(8) monopole and quadrupole pairing model is shown to be unusual in that there is no corresponding group generated only by number-conserving operators. Rather, the SO(7) symmetry is manifested in terms of number-conserving operators only by taking a particular combination of the Casimir operators appropriate for the other subgroup chains.