Neutrino Mass Generation in SO(4) Model

Generation of neutrino mass in SO(4) model is proposed here. Thealgebraic structure of SO(4) is same as to that of SU(2)_L ×SU(2)_R. It is shown that the spontaneous symmetry breaking results three massive as well as three massless gauge bosons. The standard model theory according to which there exist three massive gauge bosons and a massless one is emergedfrom this model. In the framework of SU(2)_L × SU(2)_R a small Dirac neutrino mass is derived. It is also shown that such mass term may vanish with a special choice. The Majorana mass term is not considered here and thus in this model the neutrino mass does not follow seesaw structure.     

The spinor representation,U(1)Γ embedding,and symmetry-breaking patterns in SO(14)

An SO(14) gauge theory with a spinor representation is presented as an extension of the flavor-unifying SU(7) model. The global Γ symmetry in the SU(7) theory becomes a local gauge symmetry as a part of the SO(14). The quarks are classified by 3 groups and the leptons by 2 groups according to the Γ quantum number. Three patterns of spontaneous symmetry breaking are considered, and only one of them is shown to be a viable choice.     

Instantons in SU(4) gauge theories

A complete set of solutions of SU(4) invariant gauge fields with SO(4) spherical symmetry (euclidian metric in space time) is obtained. It is shown that the solutions fall into two non equivalent classes following a spinor or vector decomposition of the four dimensional representation of SU(4) in SO(4). The energy of the first case and hence the topological quantum number are twice those of the second case.     

N = 4 supergravity theory with local SU(2) × SU(2) invariance

N = 4 supergravity theory has been formulated in two different equivalent forms, which may be expected to become inequivalent when the internal symmetry is gauged. The extension of the first form to include local SO(4) internal symmetry is known. In this paper the extension of the second form to local SU(2) × SU(2) invariance is given, and is indeed inequivalent to the first form. The second form is in general parity non-conserving, while both forms have scalar field potentials that are unbounded from below.     

群表示论的物理方法(Ⅴ)——SU3?SO3和SU4?SU2×SU2分类基

本文给出了核物理中常用的SU₃?SO₃(f=1—6)和SU₄?SU₂×SU₂波函数在Gelfand表象中的展开系数。 关键词：     

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.     

Properties of SO(8) extended supergravity

The conjectured SU(8) invariance of the field equations of SO(8) extended supergravity is used to elucidate the general structure of the extended theories. Due to the representation content of the spinless fields this does not lead to a complete determination of the theory, as was the case for N = 4. The non-polynomial modifications by spinless fields are given in terms of a number of SU(8) covariant tensors, for which various identities are derived and discussed.     

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.     

Simultaneous dimerization and SU(4) symmetry breaking of 4-color fermions on the square lattice

Using infinite projected entangled-pair states, exact diagonalization, and flavor-wave theory, we show that the SU(4) Heisenberg model undergoes a spontaneous dimerization on the square lattice, in contrast with its SU(2) and SU(3) counterparts, which develop Néel and three-sublattice stripelike long-range order. Since the ground state of a dimer is not a singlet for SU(4) but a 6-dimensional irreducible representation, this leaves the door open for further symmetry breaking. We provide evidence that, unlike in SU(4) ladders, where dimers pair up to form singlet plaquettes, here the SU(4) symmetry is additionally broken, leading to a gapless spectrum in spite of the broken translational symmetry.     

The hidden SO(4) symmetry of general SU(2) thirring models

General four-fermion interactions in two dimensions with SU(2) invariance are shown to possess a hidden SO(4) symmetry. As a consequence physical states belong to irreducible representations of the two commuting O(3) subgroups and their interactions decouple accordingly. Two independnet stable trajectories of the renormalization group are shown to exist perturbatively and are consistently reproduced by abelian bosonization.     

A chiral SU(4) × SU(4) gauge theory of weak and electromagnetic interactions

A lepton hadron analogy is considered based on the gauge group SU(4)_L × SU(4)_R × U(1), which is broken entirely spontaneously. The model satisfies the physical requirements of the V-A theory, muon-electron universality, no neutral strangeness changing currents, the Cabibbo structure for the SU(3) currents, and triangle anomalies can be avoided. The contribution of the existing neutral currents to various neutrino processes are calculated.     

A study of SU(3) × SU(2) × U(1) × U(1) as an intermediate energy subgroup of SO(10)

We analyze several patterns of symmetry breaking of SO(10) where SU(3)_c × SU(2) × U(1) × U(1) is an intermediate energy subgroup. Using constraints from the renormalization group and data from neutral-current experiments we show that if the only Higgs used in the low-energy breaking of the theory are those which can give mass to fermions then the possibility of a low intermediate mass scale is ruled out.     

On the fermion spectrum of spontaneously generated fuzzy extra dimensions with fluxes

We consider certain vacua of four‐dimensional SU(N) gauge theory with the same field content as the 𝒩 = 4 supersymmetric Yang‐Mills theory, resulting from potentials which break the 𝒩 = 4 supersymmetry as well as its global SO(6) symmetry down to SO(3) × SO(3). We show that the theory behaves at intermediate scales as Yang‐Mills theory on M⁴ × S_L² × S_R², where the extra dimensions are fuzzy spheres with magnetic fluxes. We determine in particular the structure of the zero modes due to the fluxes, which leads to low‐energy mirror models.     

Exact SU(n) instantons with cylindrical symmetry

We construct SO(3) symmetric, irreducible instantons in an SU(n) gauge theory. The solutions are symmetric with respect to J = ?ir × ? + T, where T spans the maximal SO(3) subalgebra of SU(n). Our ansatz as well as the resulting self dual equations are closely related to those for monopoles.     

Gauged N = 4 supergravities in five dimensions and their magnetovac backgrounds

Gauged N = 4 supergravity theories with Yang-Mills symmetry SU(2) × U(1) are constructed in five dimensions. As in four dimensions, the presence of a nonsimple gauge group leads to the existence of three distinct theories, depending (in five dimensions) on the values of the SU(2) and U(1) coupling constants. Two of the theories are distinguished by the relative sign of the coupling constants; one of these has a vacuum state exhibiting the full N = 4 anti-de Sitter supersymmetry SU(2,2|2), while the other has a scalar potential with no critical points. The third theory, in which the SU(2) coupling constant is taken to be zero, has vanishing scalar potential. This leads to vacua with spontaneously broken supersymmetry and zero cosmological constant, admitting compactification to four dimensions. All three theories possess “magnetovac” ground states with residual supersymmetry and hence presumably stable. Several of these may be interpreted as four-dimensional cosmological models.     

Fermionic Magnons, non-Abelian spinons, and the spin quantum Hall effect from an exactly solvable spin-1/2 Kitaev model with SU(2) symmetry

We introduce an exactly solvable SU(2)-invariant spin-1/2 model with exotic spin excitations. With time reversal symmetry (TRS), the ground state is a spin liquid with gapless or gapped spin-1 but fermionic excitations. When TRS is broken, the resulting spin liquid exhibits deconfined vortex excitations which carry spin-1/2 and obey non-Abelian statistics. We show that this SU(2) invariant non-Abelian spin liquid exhibits the spin quantum Hall effect with quantized spin Hall conductivity σ(xy)(s)=?/2π, and that the spin response is effectively described by the SO(3) level-1 Chern-Simons theory at low energy. We further propose that a SU(2) level-2 Chern-Simons theory is the effective field theory describing the topological structure of the non-Abelian SU(2) invariant spin liquid.     

Wilson loops for U(4) and SU(4) lattice gauge theories in four dimensions

Monte Carlo simulations are used to calculate Wilson loops for pure U(4) and SU(4) gauge theories on a 6⁴ lattice. The first-order phase transitions previously observed in the average action per plaquette for U(4) and SU(4) is also seen in the string tension. U(4) and SU(4) color seem to be confined while U(4) charge in U(4) appears to be deconfined.     

On-shell and conformal N = 4 supergravity in superspace

We discuss the superspace geometries which are necessary to describe on-shell O(4) and SU(4) supergravity. The relation of central charge field strengths to physical spin-zero fields is exhibited and a “new” O(4) theory is shown to exist. The version of SU(4) supergravity which uses an antisymmetric tensor gauge field is found to require modifications of ordinary superspace. Finally the Poincaré supergeometry which admits the conformal N = 4 supermultiplet is constructed. It is shown that consistency of the Bianchi identities implies the existence of dimension zero auxiliary fields which are components of a non-linear multiplet.     

Multi-component fractional quantum Hall states in graphene: SU(4) versus SU(2)

Because of the spin and Dirac-valley degrees of freedom, graphene allows the observation of one-, two- or four-component fractional quantum Hall effects in different parameter regions. We address the stability of various states in the SU(2) and SU(4) limits. In the SU(4) limit, we predict that new low-energy Goldstone modes determine the stability of the fractional quantum Hall states at 2/5, 3/7, etc; SU(4) skyrmions are not found to be relevant for the low-energy physics. These results are discussed in light of experiments.     

q-Deformed SU(1,1) ⊗ SO(6) Spectra of Interacting s,d Bosons in Nuclei

The quantum groups SU_q(1,1) and SU_q(2) are used to describe the interacting s, d bosons system which hae the q-deformed SU(1,1) ⊗ SO(6) dynamic symmetry and a Hamiltonian similar to that of O(6)-limit in the interacting boson model is constructed. Three regions of q-number are taken to analyze the influences of deformation on the deformed SU(1,1) ⊗ SO(6) spectra. It is found that the deformation parameter has important influences on the higher excited states within a quasi- rotational band. Yt isotopes with O(6) characteristics are investigated.