Towards a realistic model of Higgsless electroweak symmetry breaking

We present a 5D gauge theory in warped space based on a bulk SU(2)L x SU(2)R x U(1)(B-L) gauge group where the gauge symmetry is broken by boundary conditions. The symmetry breaking pattern and the mass spectrum resemble that in the standard model (SM). To leading order in the warp factor the rho parameter and the coupling of the Z (S parameter) are as in the SM, while corrections are expected at the level of a percent. From the anti-de Sitter (AdS) conformal field theory point of view the model presented here can be viewed as the AdS dual of a (walking) technicolorlike theory, in the sense that it is the presence of the IR brane itself that breaks electroweak symmetry, and not a localized Higgs on the IR brane (which should be interpreted as a composite Higgs model). This model predicts the lightest W, Z, and gamma resonances to be at around 1.2 TeV, and no fundamental (or composite) Higgs particles.     

Z(N) topological excitations in Yang-Mills theories: duality and confinement

We investigate the properties of Z(N) topological excitations in Wilson's lattice formulation of SU(N) Yang-Mills theories. We exhibit the Z(N) topological excitations as exact classical solutions on the lattice. After giving detailed qualitative discussions about the Z(N) excitations and their relevance to confinement, we investigate the Z(N) lattice gauge theories with the Wilson action and show that Z(2), Z(3) and Z(4) models are self-dual systems. (The self-duality of the Z(2) case has been known previously.) This property enables us to locate the critical points exactly in those systems under the assumption that the phase transition occurs at only one point in the coupling constant space. We then derive the effective action for the Z(N) topological excitations in the lattice SU(N) Yang-Mills theories in the steepest descent approximation. The critical coupling constants in the SU(N) models corresponding to the phase transition caused by the Z(N) excitations are estimated by using the information on the Z(N) models with the Wilson action. It is quite probable that the estimated value $\text{g}{}_{\mathrm{<mtext>r</mtext>}}{}^2\text{/4π}{}^2\text{～}\text{1}\text{31}$ (for SU(3)) is an upper bound. This indicates that the Wilson model of the SU(3) gauge field can be effective action of the QCD gluons which exhibit permanent quark confinement and, at the same time, freedom up to the distance characterized by the energy, at least, ～1 TeV.     

The Anomaly Coupling of Axigluon and Technicolor Neutral Pseudo Goldstone Bosons

By gauging the anomaly terms according to the gauge group SU(3)_cl x SU(3)_cr × SU(2)_l × U(l)_Y in the technicolor theory, we obtain various possibld anomaly vertices involving technicolor pseudo Goldstone boson and gauge boson (γ, Z, g, g_A). We estimate the decay rates of g_A → gP⁰, g_A → P_A⁰³γ and g_A → P_A⁰³Z.     

A Schwarzschild-like model for baryons

We present a toy model of baryons using singular solutions of the SU(2) Yang-Mill-Higgs (YMH) field equations, which bears some similarity to the Schwarzschild solution of general relativity. The SU (2) solutions are used as a background field into which a scalar, SU (2) test particle is placed. This can be compared to placing an electrically charged particle in a Coulomb background field, except the SU (2) YMH solutions are singular on a spherical membrane thus trapping (confining) the test particle inside the sphere in a manner similar to certain bag models of baryons. An interesting consequence of this model is that the composite system is a fermion even though the original Lagrangian contains only bosonic fields.     

Phase structure of QCD at high temperature with massive quarks and finite quark density: A Z(3) paradigm

The confinement/deconfinement phase transition in SU(3) lattice gauge theories at high temperatures is analogous to that of the Z(3) gauge theories. We study various Z(3) gauge-matter theories that result from replacing the gauge group SU(3) with its center Z(3). We include large-mass fermions in the Wilson formulation and allow a chemical potential. We show that in the limit of strong coupling and high temperature the (3 + 1)-dimensional theory becomes a three state, three-dimensional Potts model with uniform external fields of real and imaginary strengths related to the fermion mass and chemical potential. By studying the phase structure of the q = 3, d = 3 Potts model with external fields we argue that the confinement/deconfinement phase transition is first order, but highly sensitive to external fields, and that it does not occur at “strong coupling” in a Z(3) gauge theory if there is a light enough fermion present. We discuss the consequences of this result for QCD.     

ELECTRO-WEAK UNIFIED TNEQRY AND RELATED PROBLEMS

The minimum SU(2)×U(1) electro-weak unified theory is described and several related problems including the connection between anomaly free and charge quantization, Kobayashi-Maskawa mixing and CP violation and Higgs sector are dis-cussed. The experimental verification minimum of SU(2)×U(1) model in low energy range is presented briefly. Physical conseguences concerning to free W and Z particles are discussed. The possibilities of the existence or gauge symmetry higher than SU(2)×U(1) for electro-weak interaction and with the minimum SU(2)×U(1) model as the first order of approximation in the low energy range are given. New phenomena involving Z Partice and their implication based on SU(2)×U(1) model are examined.     

Dynamical symmetry breaking of extended gauge symmetries

We construct asymptotically free gauge theories exhibiting dynamical breaking of the left-right gauge group G(LR)=SU(3)(c) x SU(2)(L) x SU(2)(R) x U(1)(B-L), and its extension to the Pati-Salam gauge group G(422)=SU(4)(PS) x SU(2)(L) x SU(2)(R). The models incorporate technicolor for electroweak breaking, and extended technicolor for the breaking of G(LR) and G422 and the generation of fermion masses. They include a seesaw mechanism for neutrino masses, without a grand unified theory (GUT) scale. These models explain why G(LR) and G422 break to SU(3)(c) x SU(2)(L) x U(1)(Y), and why this takes place at a scale (approximately 10(3) TeV) large compared to the electroweak scale, but much smaller than a GUT scale.     

Topological features of the nonlinear sigma model with Hopf term using chiral lagrangians

We rewrite the O(3) nonlinear sigma model in 2 + 1 dimensions in terms of SU(2) matrices, thereby solving the constraint. The lagrangian has the symmetry SU(2)_Global×U(1)_Local. Static soliton solutions to this lagrangian have energy 4πN as usual. We then show that the Hopf instantons, in the formalism of principle chiral fields, are just the skymions of QCD in 3 + 1 dimensions.     

Magnetic monopoles in SU(3) and SU(2) gauge theories without Higgs' scalars

We show that certain known singular solutions for pure SU(3) Yang-Mills theory carry magnetic charges with respect to both U(1) subgroups of SU(3). A topological characterisation in terms of monopoles is given to the SU(2) singular solutions of Wu and Yang.     

Observable N-N oscillation in high scale seesaw models

We discuss a realistic high scale (nu(B-L) approximately 10(12) GeV) supersymmetric seesaw model based on the gauge group SU(2)L x SU(2)R x SU(4)c where neutron-antineutron oscillation can be in the observable range. This is contrary to the naive dimensional arguments which say that tau(N-N) is proportional to nu(B-L)5 and should therefore be unobservable for seesaw scale nu(B-L) > or = 10(5) GeV. Two reasons for this enhancement are (i) accidental symmetries which keep some of the diquark Higgs masses at the weak scale and (ii) a new supersymmetric contribution from a lower dimensional operator. The net result is that tau(N-N) is proportional to nu(B-L)2 nu(wk)3 rather than nu(B-L)5. The model also can explain the origin of matter via the leptogenesis mechanism and predicts light diquark states which can be produced at LHC.     

On Spin(7) holonomy metric based on SU(3)/U(1): II

We continue the investigation of Spin(7) holonomy metric of cohomogeneity one with the principal orbit SU(3)/U(1). A special choice of U(1) embedding in SU(3) allows more general metric ansatz with five metric functions. There are two possible singular orbits in the first-order system of Spin(7) instanton equation. One is the flag manifold SU(3)/T² also known as the twistor space of CP(2) and the other is CP(2) itself. Imposing a set of algebraic constraints, we find a two-parameter family of exact solutions which have SU(4) holonomy and are asymptotically conical. There are two types of asymptotically locally conical (ALC) metrics in our model, which are distinguished by the choice of S¹ circle whose radius stabilizes at infinity. We show that this choice of M theory circle selects one of the possible singular orbits mentioned above. Numerical analyses of solutions near the singular orbit and in the asymptotic region support the existence of two families of ALC Spin(7) metrics: one family consists of deformations of the Calabi hyper-Kähler metric, the other is a new family of metrics on a line bundle over the twistor space of CP(2).     

Deformations of the embedding of the SU(2) monopole solution in SU (3)

This paper is concerned with static Yang-Mills-Higgs fields, in the Prasad-Sommerfield limit of no Higgs self-interaction. One can obtain SU (3) multipole solutions from SU(2) solutions by embedding, in several different ways. In some of these cases, the embedding belongs to a family of SU(3) solutions that are not all embeddings; in other words, some embeddings can be deformed into non-embeddings. The simplest case, an embedding of the SU(2) spherically symmetric monopole, is studied with the aid of the twistor construction procedure. The family of axially symmetric SU(3) solutions to which it belongs is described.     

Z′ mass limits,masses and coupling of higgs bosons,and Z′ decays in an E6 superstring based model

We demonstrate that current phenomenological constraints on Z-Z′ mixing for an E₆ grand unified group with low energy gauge group SU(2)_L×U(1)_Y×U(1)_Y, allow only a narrow range of Higgs vacuum expectation values consistent with possibilities favored by renormalization group expectations. Modest improvements in bounds on this mixing will lead to substantial bounds on the Z′ mass if alternative renormalization group solutions are not found. We then explore the constraints upon relations between Higgs masses in this model. In addition we explore the couplings of these Higgs to the gauge particles of the theory and emphasize the associated implications for Higgs detection in decays of the Z′.     

Generalised actions for lattice gauge models

We consider simple modifications of the conventional Wilson action for lattice gauge theory. An SU(2) action is defined on “plaquettes” of 2×1 links. It is found to possess phase transitions in three- and four-dimensional realisations of the model. A similar model with gauge group Z(2) is also studied, and found to have two phases in three and four dimensions. We discuss the phase structure of Z(N) gauge models in four dimensions with several coupling constants and present phase diagrams for Z(4), Z(5) and Z(6).     

Squeezed Number State Solutions of Generalized Two-Mode Harmonic Oscillators Model： an Algebraic Approach

Some analytical solutions of generalized two-mode harmonic oscillators model are obtained by utilizing an algebraic diagonalization method. We find two types of eigenstates which are formulated as extended SU(1,1), SU(2) squeezed number states respectively. Some statistical properties of these states are also discussed.     

Squeezed Number State Solutions of Generalized Two-Mode Harmonic Oscillators Model:an Algebraic Approach

Some analytical solutions of generalized two-mode harmonic oscillators model are obtained by utilizing an algebraic diagonalization method. We find two types of eigenstates which are formulated as extended SU(1,1), SU(2)squeezed number states respectively. Some statistical properties of these states are also discussed.     

A classification of compactifying solutions for d =11 supergravity

Supergravity in eleven dimensions is known to have classical solutions of the type (anti-de Sitter space-time) × (7-dimensional Einstein space). We give a list of all homogeneous 7-manifolds which admit an Einstein metric. Known solutions are reviewed, with some emphasis on the SU(3) × SU(2) × U(1) compactifications. Their topology is discussed in detail.The list includes three new solutions, with symmetry groups SU(3) × SU(2), SO(5) and SO(5) × U(1). The first solution has no supersymmetry, while the second and third yield respectively N = 1 and N = 2 supersymmetry in four dimensions. The last two solutions may be extended to solutions with nonzero internal photon curl, breaking all supersymmetry.The existence of a spin structure on homogeneous manifolds $\text{G}\text{H}$ is discussed and related to topological properties of $\text{G}\text{H}$. As an illustration, we treat the coset spaces SU(m + 1) × SU(n + 1)/SU(m) × SU(n) × U(1), which include the spaces with SU(3) × SU(2) × U(1) symmetry.     

Exactly solvable model for isospin S=3/2 fermionic atoms on an optical lattice

We propose an exact solution of a model describing a low energy behavior of cold isospin S=3/2 fermionic atoms on a one-dimensional optical lattice. Depending on the band filling the effective field theory has a form of a deformed Gross-Neveu model with either O(7)x Z2 (half filling) or U(1) x O(5) x Z2 symmetry.     

The phase structure of mixed lattice gauge theories

The mixed compact-non-compact U(1) model is shown to be equivalent to a compact U(1) Higgs model. It is argued that the mixed SO(3)-SU(2) model is dual to an SO(3) gauge theory coupled to a scalar field in the fundamental representation. The degrees of freedom are Z(2) monopoles and charges or, in a dual picture, monopoles and loops. This picture is supported by a Monte Carlo calculation. The implications for the SU(2) transition region are discussed.     

Transfer matrix for the open chain from giant gravitons

We construct the transfer matrix for the open chain with the centrally extended SU(2|2) symmetry attached to the so called Z=0 giant graviton brane. Using the reflection equations, unitarity property and crossing property, we show that this model is integrable.