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.     

Theta-terms in nonlinear sigma-models

We trace the origin of θ-terms in nonlinear σ-models as a nonperturbative anomaly of current algebras. The nonlinear σ-models emerge as a low energy limit of fermionic σ-models. The latter describe Dirac fermions coupled to chiral bosonic fields. We discuss the geometric phases in three hierarchies of fermionic σ-models in space-time dimension (d+1) with chiral bosonic fields taking values on d-, d+1-, and d+2-dimensional spheres. The geometric phases in the first two hierarchies are θ-terms. We emphasize a relation between θ-terms and quantum numbers of solitons.     

Noncommutative supergeometry, duality and deformations

Following Lett. Math. Phys. 50 (1999) 309, we introduce a notion of Q-algebra that can be considered as a generalization of the notion of Q-manifold (a supermanifold equipped with an odd vector field obeying {Q,Q}=0). We develop the theory of connections on modules over Q-algebras and prove a general duality theorem for gauge theories on such modules. This theorem containing as a simplest case SO(d,d,Z)-duality of gauge theories on noncommutative tori can be applied also in more complicated situations. We show that Q-algebras appear naturally in Fedosov construction of formal deformation of commutative algebras of functions and that similar Q-algebras can be constructed also in the case when the deformation parameter is not formal.     

空心圆柱形永磁体内径对单畴GdBCO超导块材磁悬浮力的影响

通过对空心圆柱形永磁体与单畴GdBCO超导体磁悬浮力的实验测量,研究了空心圆柱形永磁体内径(d)的变化对超导体磁悬浮力的影响.结果发现,当空心圆柱形永磁体内径从0 mm增加到26 mm时,超导磁悬浮力大小与空心圆柱形永磁体内径有着密切关系(最小测量间距Z=2 mm),所有超导磁悬浮力曲线都存在磁滞现象.随着空心圆柱形永磁体内径的增大,最小间距处超导磁悬浮力逐渐减小,从d=0 mm时的14.8 N减小为d=26 mm时的-0.1 N,d≥20 mm时,最小间距处超导磁悬浮力出现负值;当0 mm≤d5 mm时,超导体最大磁悬浮力出现在最小间距处,d≥5 mm时,超导磁悬浮力先增大后减小,最大超导磁悬浮力产生的位置随着内径的增大而变大.研究表明:只有科学合理地设计永磁体结构参数,才能获得较大的磁场强度,提高超导磁悬浮力特性.该结果对设计并优化磁悬浮轴承系统、环形轨道和超导体的实际应用具有一定的指导意义.     

Holes in a quantum antiferromagnet: A formalism and some exact results

This is a detailed version of an earlier communication in which a theory of hole motion in a quantum antiferromagnet was developed and some exact results obtained in d=1. In this picture, hole motion is very naturally restricted to sublattice A or B of a bipartite lattice. Holes in A or B behave like oppositely charged particles coupled to a gauge field driven by the antiferromagnetic fluctuations of the medium. The general picture is studied in detail for d=1, for a finite concentration of holes. The continuum theory is that of a massless Dirac fermion coupled to the nonlinear sigma model field via a gauge coupling. It is found that holes can wipe out the topological θ term, reduce the power law antiferromagnetic correlations to exponentials and show a divergent superconducting susceptibility. The style of the paper is rather pedagogical and intended for a broad readership.     

N=1 formulation of general N=2 Yang-Mills supergravity couplings

We formulate general interactions of an N=2 Yang-Mills supermultiplet coupled to N=2 supergravity in terms of N=1 invariant functions. We show that the N=2 scalar potential of the complex scalar fields in the adjoint representation, superpartners of the Yang-Mills gauge fields, splits into a conventional gauge contribution as well as in a superpotential term contribution proportional to the SO(2) gauge coupling of N=2 de Sitter supergravity. The relation of these results to the σ model structure of N4 extended supergravities is also discussed, particularly in connection with the coset disintegration of scalar manifolds.     

Order-disorder criticality, wetting, and morphological phase transitions in the irreversible growth of far-from-equilibrium magnetic films

An exhaustive numerical investigation of the growth of magnetic films in confined (d+1)-dimensional stripped geometries (d=1,2) is carried out by means of extensive Monte Carlo simulations. Films in contact with a thermal bath at temperature T, are grown by adding spins having two possible orientations and considering ferromagnetic (nearest-neighbor) interactions. At low temperatures, thin films of thickness L are constituted by a sequence of well-ordered domains of average length l_DL. These domains have opposite magnetization. So, the films exhibit “spontaneous magnetization reversal” during the growth process. Such reversal occurs within a short characteristic length l_R, such that l_Dl_RL. Furthermore, it is found that for d=1 the system is non-critical, while a continuous order-disorder phase transition at finite temperature takes place in the d=2 case. Using standard finite-size scaling procedures, the critical temperature and some relevant critical exponents are determined. Finally, the growth of magnetic films in (2+1) dimensions with competing short-range magnetic fields acting along the confinement walls is studied. Due to the antisymmetric condition considered, an interface between domains with spins having opposite orientation develops along the growing direction. Such an interface undergoes a localization–delocalization transition that is the precursor of a wetting transition in the thermodynamic limit. Furthermore, the growing interface also undergoes morphological transitions in the growth mode. A comparison between the well-studied equilibrium Ising model and the studied irreversible magnetic growth model is performed throughout. Although valuable analogies are encountered, it is found that the non-equilibrium nature of the latter introduces new and rich physical features of interest.     

Nonperturbative dynamics of noncommutative gauge theory

We present a nonperturbative lattice formulation of noncommutative Yang–Mills theories in arbitrary even dimension. We show that lattice regularization of a noncommutative field theory requires finite lattice volume which automatically provides both an ultraviolet and an infrared cutoff. We demonstrate explicitly Morita equivalence of commutative U(p) gauge theory with p·n_f flavours of fundamental matter fields on a lattice of size L with twisted boundary conditions and noncommutative U(1) gauge theory with n_f species of matter on a lattice of size p·L with single-valued fields. We discuss the relation with twisted large N reduced models and construct observables in noncommutative gauge theory with matter.     

N=2 6-dimensional supersymmetric E6 breaking

We study the N=2 supersymmetric E₆ models on the 6-dimensional space–time where the supersymmetry and gauge symmetry can be broken by the discrete symmetry. On the space–time M⁴×S¹/(Z₂×Z₂′)×S¹/(Z₂×Z₂′), for the zero modes, we obtain the 4-dimensional N=1 supersymmetric models with gauge groups SU(3)×SU(2)×SU(2)×U(1)², SU(4)×SU(2)×SU(2)×U(1), and SU(3)×SU(2)×U(1)³ with one extra pair of Higgs doublets from the vector multiplet. In addition, considering that the extra space manifold is the annulus A² and disc D², we list all the constraints on constructing the 4-dimensional N=1 supersymmetric SU(3)×SU(2)×U(1)³ models for the zero modes, and give the simplest model with Z₉ symmetry. We also comment on the extra gauge symmetry breaking and its generalization.     

Anisotropic percolation and the d-dimensional surface roughening problem

We review recent numerical simulations of several models of interface growth in d-dimensional media with quenched disorder. These models belong to the universality class of anisotropic diode-resistor percolation networks. The values of the roughness exponent δ=0.63±0.01 (d=1+1) and δ=0.48±0.02 (d=2+1) are in good agreement with our recent experiments. The values of δ in higher dimensions (δ=0.38±0.03 in d=4 and δ=0.27±0.05 in d=5) do not support a recent theoretical conjecture.     

Effect of bare mass on the Hosotani mechanism

It is pointed out that the existence of bare mass terms for matter fields changes gauge symmetry patterns through the Hosotani mechanism. As a demonstration, we study an SU(2) gauge model with massive adjoint fermions defined on M⁴S¹. It turns out that the vacuum structure changes at certain critical values of mL, where m (L) stands for the bare mass (the circumference of S¹). The gauge symmetry breaking patterns are different from models with massless adjoint fermions. We also consider a supersymmmetric SU(2) gauge model with adjoint hypermultiplets, in which the supersymmetry is broken by bare mass terms for the gaugino and squark fields instead of the Scherk–Schwarz mechanism.     

On generalized condensation in the free boson gas

We investigate the free boson gas with Dirichlet boundary conditions in d-dimensional Euclidean space. For d > 2 we find three types of condensation when the mean density ρ exceeds a critical value ρ_c, depending on how the bulk limit is taken.     

4p-4d fano-like resonance in rhodium

Photoemission measurements of Rh films in the photon energy range 40–120 eV show that the 4p-4d intrashell interaction has a Fano-like resonance. The 4d photoemission intensity goes through a sharp dip in the vicinity of the 4p⁶4dⁿ+hv → 4p⁵4dⁿ⁺¹ threshold followed by a resonant enhancement before decreasing again. All parts of the 4d band show the same resonant behavior in contrast to previous resonant photoemission results. The resonant behavior of Rh is compared with Co which is the 3d analog of Rh.     

A simple derivation of the overlap Dirac operator

We derive the vector-like four-dimensional overlap Dirac operator starting from a five-dimensional Dirac action in the presence of a delta-function space–time defect. The effective operator is obtained by first integrating out all the fermionic modes in the fixed gauge background, and then identifying the contribution from the localized modes as the determinant of an operator in one dimension less. We define physically relevant degrees of freedom on the defect by introducing an auxiliary defect-bound fermion field and integrating out the original five-dimensional bulk fields.     

Infrared reflectivity and dielectric permeability of ultra-thin Cu and Al films

In this report we present an experimental investigation of the reflectivity (R) and the dielectric permeability () for Cu and Al ultra-thin films ranging in thickness from a few monolayers to 12 nm at infrared and visible wavelengths. The metal films were prepared by RF-sputtering on SiO₂ (glass) and Si substrates. IR reflectivity was measured at 9.2 μm, while was measured with the help of laser ellipsometer at a wavelength of 632.8 nm. Two types of oscillations on R(d) and (d) were discovered for two thickness regions determined by the critical thickness value d*. Oscillations at d<d* with periods near 0.3 nm for Al and Cu films were observed on R(d) and (d) due to quantum sized effects (QSEs). At d>d* (thickness between 6–12 nm) we discover a new type of strong oscillation of R(d) and (d) with an oscillating period of 0.2 nm. For thickness larger than 12 nm all the oscillations tend to disappear and R and behave almost as their volume values. A possible explanation for the appearance of these two kinds of oscillations is based on the introduction of the critical film thickness d*.     

Critical dynamics of a stochastic n-vector model below Tc

The dynamic properties of a stochastic n-vector model are investigated for T < T_c in d=4−ε dimensions. Besides the non-conserved order parameter the model involves also the conserved densities of generators of the symmetry group O(n). We calculate the excitation spectra of those conserved densities and the transverse fluctuations of the order parameter to linear order in ε in the hydrodynamic region kξ1. The propagating modes have linear dispersion and quadratic damping in accordance with the phenomenological theory. The relaxing modes, however, exhibit non-hydrodynamic wavenumber dependence with a relaxation rate ω_k ∞ k^d/2.     

Explicit counteraction algorithms in higher dimensions

Using the background field method we construct algorithms for the one-loop counterterms of a field theory in a space-time of dimension 2, 4, 6, 8 or 10. From the d = 6 algorithm we demonstrate the one-loop finiteness of N = 2 supersymmetric Yang-Mills theories and also N = 1 Yang-Mills theory. All other N = 1 Yang-Mills theories + N = 1 matter theories in d = 6 are shown to have a divergent one-loop S-matrix.

We also present partial results for two- and three-loop algorithms in d = 6 and d = 4 respectively.     

Finite-size scaling properties of the damage distance and dynamical critical exponent for the Ising model

With the damage spreading method, scaling properties of the damage distance on the Ising model with heat bath dynamics are studied numerically. With the parallel flipping scheme, the scaling curves fall on two curves, which depend on the odd or even lattice sizes. The both scaling curves give the consistent dynamical exponent as z = 2.16±0.04 for d = 2 and z = 2.09±0.05 for d = 3, respectively. By shifting one of them, two curves overlap each other perfectly. Meanwhile, all the scaling curves obtained by single-spin flipping processes (with different odd or even lattice sizes) fall on a single curve, from which the consistent dynamical critical exponent with the parallel scheme is obtained z = 2.18±0.02 for d = 2 and z = 2.08±0.04 for d = 3.     

The thermodynamics of purely elastic scattering theories and conformal perturbation theory

We discuss the thermodynamic Bethe ansatz, and explain how it allows one to reduce the infinite-volume thermodynamics of a (1 + 1)-dimensional purely elastic scattering theory to the solution of a set of integral equations for the one-particle excitation energies. The free energy at zero chemical potential(s) and temperature T is related to the ground state energy E₀(R) of the theory on a cylinder of circumference R = 1/T. E₀(R) determines properties of the CFT describing the UV limit of the given massive theory. These include the central charge (which we investigated in earlier work), the scaling dimension d of the conformal field whose perturbation leads to the massive theory, the coefficients in the conformal perturbation theory (CPT) expansion of E₀(R) in powers of R^2−d, and the bulk term in the CPT calculation of the ground-state energy. We determine the bulk term analytically, and obtain numerically the first six coefficients in the expansion of E₀(R) for many purely elastic scattering theories, including the scaling limit of the T = T_c Ising model in a magnetic field. The perfect agreement with (more limited) direct CPT results provides further strong support for the identification of these theories as specific perturbed CFTs. We suggest that the singularities of E₀(R), the first of which is responsible for the finite radius of convergence of CPT, are square-root branch points and related to the zeros of the partition function of the corresponding lattice model.