Inflation and cosmic strings in models with dynamical symmetry breaking

We derive the effective action for the composite field which in dynamical symmetry breaking plays the role of the Higgs field. We show that this effective action does not give rise to inflation. It is, however, possible to obtain topological defects such as cosmic strings. There will be fermionic zero modes trapped on the strings, and the strings will therefore be superconducting in a generalized sense.     

Electron fractionalization in two-dimensional graphenelike structures

Electron fractionalization is intimately related to topology. In one-dimensional systems, fractionally charged states exist at domain walls between degenerate vacua. In two-dimensional systems, fractionalization exists in quantum Hall fluids, where time-reversal symmetry is broken by a large external magnetic field. Recently, there has been a tremendous effort in the search for examples of fractionalization in two-dimensional systems with time-reversal symmetry. In this Letter, we show that fractionally charged topological excitations exist on graphenelike structures, where quasiparticles are described by two flavors of Dirac fermions and time-reversal symmetry is respected. The topological zero modes are mathematically similar to fractional vortices in p-wave superconductors. They correspond to a twist in the phase in the mass of the Dirac fermions, akin to cosmic strings in particle physics.     

Momentum space topology of fermion zero modes brane

We discuss fermion zero modes within the 3+1 brane, i.e., the domain wall between the two vacua in 4+1 spacetime. We do not assume relativistic invariance in 4+1 spacetime or any special form of the 4+1 action. The only input is that the fermions in bulk are fully gapped and are described by a nontrivial momentum-space topology. Then the 3+1 wall between such vacua contains chiral 3+1 fermions. The bosonic collective modes in the wall form the gauge and gravitational fields. In principle, this universality class of fermionic vacua can contain all the ingredients of the Standard Model and gravity.     

Bounds on Higgs and top quark masses from vacuum stability(degeneracy) with gravitational contributions

Based on the two-loop RGE of standard model gauge, top-Yukawa as well as scalar quartic couplings with full one-loop gravitational contributions in harmonic gauge, we study the constraints on the Higgs and top quark mass from the requirement that the other degenerate vacua at the Planck-dominated region exists. Our numerical calculations show that nature will not develop the other degenerate vacua at the Planck-dominated region with current Higgs and top quark masses. On the other hand, requiring the existence of the other degenerate vacua at the Planck-dominated region will constrain the Higgs and top mass to lie at approximately 130 and 174 Ge V, respectively.     

Finite-temperature behavior of the lattice abelian Higgs model

We study phase transitions in the lattice version of the abelian Higgs model, a model which can exhibit both spontaneous symmetry breaking and confinement. When the Higgs charge is the basic U(1) unit, we find that the Higgs and confinement regions are not separated by a phase transition and form a single homogenous phase which we call the total screening phase. The model does not undergo a symmetry restoring phase transition at finite temperature.If the Higgs charge is some multiple of the basic unit the model follows the conventional wisdom: there are 3 phases (normal, Higgs and confinement) at zero temperature, two of which disappear above some critical point. We apply the lessons learned from the lattice Higgs model to understand the behavior of the weak interactions at high temperature.In a long appendix we give an intuitive physical picture for the Polyakov-Susskind quark liberating phase transition and show that it is related to the Hagedorn spectrum of a confining model. We end with a collection of effective field theory approximations to various lattice theories.     

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.     

Searching singlet extensions of the supersymmetric standard model in Z 6−II orbifold compactification of heterotic string

We search for supersymmetric standard model realizations with extra singlets and extra U(1) using the heterotic string compactification on the Z _6?II orbifold with two Wilson lines. The effective superpotential produced through the vacuum restabilization mechanism is examined for three representative Pati–Salam string models obtained in the literature. An automated selection of semi-realistic vacua along flat directions in the non-Abelian singlet modes field space is performed by requiring the presence of massless pairs of electroweak Higgs bosons having trilinear superpotential couplings with massless singlet modes and the decoupling of color triplet exotic modes needed to suppress B and L number violating processes.     

The magnetic charges of stable self-dual monopoles

Gauge theories, in which the Higgs field lies in the adjoint representation, has zero self-coupling (the BPS limit) and leads to an exact symmetry of the local form U(1) × K with K semisimple, are considered. The charges of potentially stable magnetic monopoles, arising as classical solutions, are analysed and it is found that they have a structure consistent with their interpretation as heavy gauge particles of an overall symmetry group dual to the original one, providing further circumstantial evidence for the duality between electric and magnetic fields in this type of theory.     

GUT breaking on M×T/(Z2×Z2′)

We construct two SU(5) models on the space–time M⁴×T²/(Z₂×Z₂′) where the gauge and Higgs fields are in the bulk and the Standard Model fermions are on the brane at the fixed point or line. For the zero modes, the SU(5) gauge symmetry is broken down to SU(3)×SU(2)×U(1) due to non-trivial orbifold projection. In particular, if we put the Standard model fermions on the 3-brane at the fixed point in model II, we only have the zero modes and KK modes of the Standard Model gauge fields and two Higgs doublets on the observable 3-brane. So, we can have the low energy unification, and solve the triplet–doublet splitting problem, the gauge hierarchy problem, and the proton decay problem.     

The string landscape: On formulas for counting vacua

We derive formulas for counting certain classes of vacua in the string/M theory landscape. We do so in the context of the moduli space of M-theory compactifications on singular manifolds with _G2$G_2$ holonomy. Particularly, we count the numbers of gauge theories with different gauge groups but equal numbers of U(1)$U(1)$ factors which are dual to each other. The vacua correspond to various symmetry breaking patterns of grand unified theories. Counting these dual vacua is equivalent to counting the number of conjugacy classes of elements of finite order inside Lie groups. We also point out certain cases where the conventional expectation is that symmetry breaking patterns by Wilson lines and Higgs fields are the same, but we show they are in fact different.     

Neutral currents and the Higgs mechanism

The consequences of assuming (i) weak and e.m. forces constitute a gauge field theory, and (ii) there are no heavy leptons, are investigated. Relative to the Weinberg model, introduction of a general spontaneous symmetry breaking system leads to a theory with one extra free parameter, namely the neutral vector boson mass. Experimental consequences are indicated. A particular Higgs system containing two multiplets is studied in detail. It is noted that parameters may be chosen such that the cosmological constant is zero before as well as after spontaneous symmetry breakdown.     

Selective modes excitation in multimode photonic crystal waveguides

We investigate modes excitation with the input field of different positions in two-dimensional multimode photonic crystal waveguides. Odd modes can be selectively excited by the input field of odd symmetry. The input field with different positions can excite different modes due to the field intensity distribution of modes. When the input field locates at the position of the zero field, intensity of waveguide modes is zero and the modes are not excited. The finite-difference time-domain method is used to obtain the excited field distributions.     

Approximate weinberg mixing

We present a model of the weak interactions in which a custodial symmetry that is not an invariance of the starting Lagrangian emerges in the effective low-energy sector of the theory. This symmetry maintains the relationM _w=M _z cos _w to all orders in the Higgs self-couplings to any required degree of accuracy, while leaving the quark mass spectrum completely unconstrained. The model is a local left-right symmetric chiral flavor gauge theory of the electroweak interactions in which the symmetry is spontaneously broken by fundamental Higgs fields which transform the same way under the chiral group as fermion Dirac and Majorana masses.     

On axially-symmetric finite-energy monopole configurations

Axially symmetric finite energy monopole configurations are investigated for the gauge group SO(3) with the Higgs field in the adjoint representation. To avoid the complications due to gauge freedom gauge invariant fields are introduced and used throughout. From topological and continuity considerations it is argued that the only regular axially symmetric magnetic charge distributions permitted are isolated charges of uniform strength and alternate sign located along the axis of symmetry. In particular, if there is only one sign, the magnetic charge must be located at a single point. For a zero Higgs potential the minimal energy (first order Bogomolny) field equations take a simple form when written in terms of the gauge-invariant fields. In general, there are nine equations for nine (axially symmetric) fields, but these reduce to five equations for five fields if a further symmetry (invariance under reflexions in planes through the axis of symmetry) is imposed. Remarkably, four of the equations are the same whether the reflexion symmetry is imposed or not, and these four equations can be completely solved in terms of a master potential. From these and the remaining equations (just one in the case of mirror symmetry) the asymptotic behaviour of the functions at large distances and in the neighbourhood of the origin (the location of the charge) is obtained and studied in some detail.     

Inflation and conformal invariance: the perspective from radial quantization

According to the dS/CFT correspondence, correlators of fields generated during a primordial de Sitter phase are constrained by three‐dimensional conformal invariance. Using the properties of radially quantized conformal field theories and the operator‐state correspondence, we glean information on some points. The Higuchi bound on the masses of spin‐s states in de Sitter is a direct consequence of reflection positivity in radially quantized CFT₃ and the fact that scaling dimensions of operators are energies of states. The partial massless states appearing in de Sitter correspond from the boundary CFT₃ perspective to boundary states with highest weight for the conformal group. Finally, we discuss the inflationary consistency relations and the role of asymptotic symmetries which transform asymptotic vacua to new physically inequivalent vacua by generating long perturbation modes. We show that on the CFT₃ side, asymptotic symmetries have a nice quantum mechanics interpretation. For instance, acting with the asymptotic dilation symmetry corresponds to evolving states forward (or backward) in “time” and the charge generating the asymptotic symmetry transformation is the Hamiltonian itself.     

Radiative seesaw mechanism and degenerate neutrinos

The radiative seesaw mechanism of Witten generates the right-handed neutrino masses in SO(10) with the spinorial 16(H) Higgs field. We study here analytically the 2nd and 3rd generations for the minimal Yukawa structure containing and Higgs representations. In the approximation of small 2nd generation masses and gauge loop domination we find the following results: (1) beta-tau unification, (2) natural coexistence between large theta(l) and small theta(q), and (3) degenerate neutrinos.     

Conformal invariance and spontaneous symmetry breaking

We study the spontaneous symmetry breaking in a conformally invariant gravitational theory. We particularly emphasize on the nonminimal coupling of matter fields to gravity. By the nonminimal coupling we consider a local distinction between the conformal frames of metric of matter fieldsand the metric explicitly entering the vacuum sector. We suppose that these two frames are conformally related by a dilaton field. We show that the imposition of a condition on the variable mass term of a scalar field may lead to the spontaneous symmetry breaking. In this way the scalar field may imitate the Higgs field behavior. Attributing a constant configuration to the ground state of the Higgs field, a Higgs conformal frame is specified. We define the Higgs conformal frame as a cosmological frame which describes the large scale characteristics of the observed universe. In the cosmological frame the gravitational coupling acquires a correct value and one no longer deals with the vacuum energy problem. We then study a more general case by considering a variable configuration for the ground state of Higgs field. In this case we introduce a cosmological solution of themodel.     

Mass relations in the two Higgs doublet model from the absence of quadratic divergences

By setting the quadratic divergences to zero, four mass relations are obtained for the Standard Model generalized to two Higgs doublets. These four mass relations are obtained most simply in terms of the original fields in the Lagrangian, before spontaneousSU(2)×U(1) symmetry breaking is applied. Unlike the case of the Standard Model, the Higgs tadpoles of the two Higgs doublet theory do not furnish a complete set of mass relations, giving only three of the four.Work supported in part by the U.S. Department of Energy under Grant DE-FG02-84ER40158     

Hierarchies from D-brane instantons in globally defined Calabi-Yau orientifolds

We construct the first globally consistent semirealistic type I string vacua on an elliptically fibered manifold where the zero modes of the Euclidean D1-instanton sector allow for the generation of nonperturbative Majorana masses of an intermediate scale. In another class of global models, a D1-brane instanton can generate a Polonyi-type superpotential breaking supersymmetry at an exponentially suppressed scale.