The topological susceptibility in SU(2) lattice gauge theory: An exploratory study

The local topological charge density of the (Monte Carlo generated) SU(2) vacuum is measured, using an algorithm that has the correct continuum limit and is not contaminated by perturbative contributions or dislocations. The resulting susceptibility, χ_t ∼ (130 MeV)⁴ (using m_ρ measurements to set physical units), is smaller than that obtained by “geometric” methods and is suppressed at small physical lattice volumes. Various systematic biases are quantified: finite volume effects, reaching equilibrium and uniqueness of the topology. The role of instantons is commented upon and an inequality between χ_t and the gluon condensate is presented. It is found that a significant fraction of the non-perturbative action resides in extended topological objects.     

Towards a semi-classical approximation of the non-linear σ-model

We consider the contribution of instantons of arbitrary topological charge to the expectation value of any observable in the CP¹ model defined on the sphere S².We replace the integration over one of the parameters of the instantons by an integration over the group of isospin transformations and carry it out explicitly by using the isospin invariance. This allows us to express the result as the expectation value of an observable of a neutral gas of 2 species of particles, computed in the grand canonical ensemble. The interactions are complicated and involve multi-body forces (2 × k, k being the topological charge).     

Slant path intensity distribution of focusing J0-correlated Schell-model vortex beams in atmospheric turbulence

The intensity distribution of the J₀-correlated Schell-model (JSM) vortex beams focused by a lens and propagation in weak-to-strong turbulent atmosphere are investigated. It is shown that the beam spreading increases with the increase in topological charge n, the source coherent length α−1, turbulent outer scale L₀ and propagation distance z. The center hollow depth of intensity distribution of the J₀-correlated Schell-model (JSM) vortex beams decrease with the increase of topological charge n, turbulent outer scale L₀ and propagation distance z or the decrease of the source coherent length α−1.     

Supersymmetric Yang-Mills,octonionic instantons and triholomorphic curves

In four-dimensional gauge theory there exists a well-known correspondence between instantons and holomorphic curves, and a similar correspondence exists between certain octonionic instantons and triholomorphic curves. We prove that this latter correspondence stems from the dynamics of various dimensional reductions of ten-dimensional supersymmetric Yang-Mills theory. More precisely we show that the dimensional reduction of the (5+1)-dimensional supersymmetric sigma model with hyper-Kähler (but otherwise arbitrary) target X to a four-dimensional hyper-Kähler manifold M is a topological sigma model localising on the space of triholomorphic maps M -+ X (or hyperinstantons). When X is the moduli space M_k of instantons on a four-dimensional hyper-Kdhler manifold K, this theory has an interpretation in terms of supersymmetric gauge theory. In this case, the topological sigma model can be understood as an adiabatic limit of the dimensional reduction of ten-dimensional supersymmetric Yang-Mills on the eight-dimensional manifold M × K of holonomy Sp(1) × Sp(1) ⊂ Spin(7), which is a cohomological theory localising on the moduli space of octonionic instantons.     

Comparison of |Q|=1 and |Q|=2 gauge-field configurations on the lattice four-torus

It is known that exactly self-dual gauge-field configurations with topological charge |Q|=1 cannot exist on the untwisted continuum four-torus. We explore the manifestation of this remarkable fact on the lattice four-torus for SU(3) using advanced techniques for controlling lattice discretization errors, extending earlier work of De Forcrand et al. for SU(2). We identify three distinct signals for the instability of |Q|=1 configurations, and show that these signals manifest themselves early in the cooling process, long before the would-be instanton has shrunk to a size comparable to the lattice discretization threshold. These signals do not appear for the individual instantons which make up our |Q|=2 configurations. This indicates that these signals reflect the truly global nature of the instability, rather than the local discretization effects which cause the eventual disappearance of the would-be single instanton. Monte-Carlo generated SU(3) gauge-field configurations are cooled to the self-dual limit using an -improved gauge action chosen to have small but positive errors. This choice prevents lattice discretization errors from destroying instantons provided their size exceeds the dislocation threshold of the cooling algorithm. Lattice discretization errors are evaluated by comparing the -improved gauge-field action with an -improved action constructed from the square of an -improved lattice field-strength tensor, thus having different discretization errors. The number of action-density peaks, the instanton size, and the topological charge of configurations is monitored. We observe a fluctuation in the total topological charge of |Q|=1 configurations, and demonstrate that the onset of this unusual behavior corresponds with the disappearance of multiple-peaks in the action density. At the same time discretization errors are minimal.     

Optimal phase steps of multi-level spiral phase plates

We analyze vortex properties of the optical beams generated by a multi-level spiral phase plate (MLSPP) and find that this kind of beams consists of vortex components with topological charges of L − kM, where k is zero or any integer, M is the level number and L is the intrinsic topological charge of the MLSPP. We proved that the orbital angular momentum of the beams generated by a MLSPP reaches its maximum only if the phase steps (or the ratio of M to L) satisfies some special conditions.     

Two dimensional gases of weight charges and SU(N) fermino theories

We analyze two dimensional gases composed of particles interacting via a Coulomb or Yakawa potential through their “non-Abelian” charges. These charges are taken to be elementary weight or root vectors of SU(N). The grand partition function of these gases is shown to be equivalent to the generating functional of sine-Gordon models with weight vectors and hence to that of SU(N) fermion models. The fermion field creates or annihilates topological solitons which have elementary weight vectors as topological quantum numbers. Then, we discuss the confinement of fermions in the SU(N) Higgs models, where instantons (Z_N vortices) constitute a Yukawa gas of weight charges. We prove that fermions are confirmed by the effects of instantons in the SU(N) Higgs models in contrast with the Abelian Higgs model.     

Radiative decays and transition form factors of strange mesons in the relativistic constituent quark model

Motivated by the recent lattice QCD results indicating that the topological charge contribution to the flavor singlet axial vector current can be traded off by the constituent quark masses, we investigate the radiative decays of pseudoscalar (π,K, η, η′), vector (ρ,K*, ω, ?) and axial vector (A ₁) mesons using a simple relativistic constituent quark model. For both simplicity and relativity, we take advantage of the distinguished features in the light-cone quantization method: (1) the Fock-state expansion of meson wavefunctions are not contaminated by the vacuum fluctuation, (2) the assignment of meson quantum numbers are given by the Melosh transformation. Except the well-known constituent quark masses of (u,d,s) quarks and the spin-averaged meson masses, the only parameter in the model is the gaussian parameter β which determines the broadness (or sharpness) of radial wavefunction. The computed decay widths and the transition form factors of ρ, ω → π(η)γ*,K* →Kγ* andA ₁ → πγ* at 0≤Q ²≤5 GeV² and π⁰(η) → γ*γ at 0≤Q ²≤3 GeV² are in a remarkably good agreement with the experimental data and the result forA ₁ ⁺ → π₊ γ* transition is quite consistent with the experiments of pion scattering on a nucleus using Primakoff effect. This model is potentially useful in the cocktail analyses of the dilepton productions in proton-proton, proton-nucleus and nucleus-nucleus collisions at SPS energies and a little above.     

Spontaneous SU(2) symmetry violation in the SU(2) L × SU(2) R × SU(4) electroweak model

A new approach to electroweak (EW) composite scalars is developed starting from the fundamental gauge interaction on high scale. The latter is assumed to have the group structure SU(2) _L × SU(2) _R × SU(4), where SU(4) is the Pati-Salam color-lepton group. The topological EW vacuum filled by instantons is explicitly constructed and the resulting equations for fermion masses exhibit spontaneous SU(2) flavor symmetry violation with possibility of very large mass ratios.     

Investigating the topological structure of quenched lattice QCD with overlap fermions using a multi-probing approximation

The topological charge density and topological susceptibility are determined by a multi-probing approximation using overlap fermions in quenched SU(3) gauge theory. Then we investigate the topological structure of the quenched QCD vacuum, and compare it with results from the all-scale topological density. The results are consistent.Random permuted topological charge density is used to check whether these structures represent underlying ordered properties. The pseudoscalar glueball mass is extracted from the two-point correlation function of the topological charge density. We study 3 ensembles of different lattice spacing a with the same lattice volume 16~3×32. The results are compatible with the results of all-scale topological charge density, and the topological structures revealed by multi-probing are much closer to all-scale topological charge density than those from eigenmode expansion.     

The large-N deconfinement phase transition in a partially reduced Eguchi-Kawal model

We construct generalized twisted Eguchi-Kawai models which for large-N reduce space-time to a lattice of arbitrary size. Large-N lattice gauge theory at finite temperature is investigated in a model on a lattice with L₀ time slices and two lattice points in very time slice. We observe the large-N deconfinement phase transition in the weak coupling region. Assuming asymptotic scaling we find a transition temperature T_c = (101±4)Λ_L.     

Specific features in the behavior of the effective mass and mobility in n-(Bi, Sb)2(Te, Se, S)3 solid solutions

The thermoelectric properties of the multicomponent solid solutions Bi_2?x Sb_xTe_3?y?z Se_yS_z with substitutions of atoms in both sublattices of Bi₂Te₃ were studied. The data obtained in studies of the galvanomagnetic effects in weak magnetic fields were used to properly take into account the change in the carrier scattering mechanisms due to the substitutions Sb → Bi, Se, and S → Te in the solid solutions. The mobility μ₀ with inclusion of the degeneracy, the effective density-of-states mass m/m ₀, and the lattice thermal conductivity κ_L were calculated. An analysis was carried out for the quantities μ₀, m/m ₀, and κ_L in the solid solutions under study as functions of the composition, carrier concentration, and temperature.     

On the tremendous effect of an electric field on the crystal lattice of quasi-one-dimensional conductors with a charge density wave

The deformation of the lattice of quasi-one-dimensional conductors with a charge density wave deformed by an electric field has been considered. In the case of the “strong” interaction between the charge density wave and lattice, the effect of the field can be compared to the usual piezoelectric effect with a tremendous piezoelectric modulus that is larger than the value in ionic crystals by a factor of L _c/λ (λ is the period of the charge density wave and L _c is the coherence length reaching several millimeters upon the sliding of the charge density wave). The interaction between the charge density wave and lattice is likely attributed to the possibility of the interband redistribution of charges (rearrangement of covalent bonds) in the process of the deformation of certain compounds with the charge density wave. The observed and expected effects provide a way of the creation of fundamentally new actuators including those of nanometer sizes.     

Analytic study of θ vacua on the lattice

A new definition of the topological charge density for four-dimensional lattice gauge theory is given. Using a systematic expansion we find a cusp in the vacuum energy at θ = π signaling the spontaneous breaking of CP there. Unlike its two-dimensional analogue (QED₂), QCD confines at θ = π. As a by-product an expression for the topological mass term for (2+1)-dimensional lattice gauge theory is obtained.     

Baryon duality solutions with the harmonic-oscillator spectrum and the amplitude signs in πN→πΔ

By constructing exact exchange-degenerate solutions of baryons with the harmonic-oscillator spectrum for a set of reactions MB→M′B′, MB → M′D′ and MD → M′D′, we investigate the duality constraints on the amplitude signs in MB → M′D′. It is shown that the amplitude signs determined by duality are consistent with those predicted by the extended version of SU(6)_W symmetry with the universal dominance of the ΔL_Z = 0 or ΔL_Z = ±1 amplitude in the mesonic transitions of the baryons.     

A statistical approach to quantum mechanics

A Monte Carlo method is used to evaluate the Euclidean version of Feynman's sum over particle histories. Following Feynman's treatment, individual paths are defined on a discrete (imaginary) time lattice with periodic boundary conditions. On each lattice site, a continuous position variable x_i specifies the spacial location of the particle. Using a modified Metropolis algorithm, the low-lying energy eigenvalues, |ψ₀(x)|², the propagator, and the effective potential for the anharmonic oscillator are computed, in good agreement with theory. For a deep double-well potential, instantons were found in our computer simulations appearing as multi-kink configurations on the lattice.     

Topology and universality in the lattice CP2 model

The topological susceptibility χ_t and the correlation length ξ in the CP² model on a two-dimensional triangular lattice are calculated by the Monte Carlo simulation method. Using variant lattice actions, we verify the universality of the dimensionless quantity χ_tξ² ～- 0.09 in the scaling region, thus indicating the presence of physical topological effects in the scaling limit. As a by-product, we obtain a combinatorial formula for the topological charge.     

Monopoles, instantons and chiral condensate in lattice QCD

We analyze the interplay of topological objects in four-dimensional QCD at finite temperature on the lattice. The distributions of color magnetic monopoles in the maximum abelian gauge are computed around instantons. Studies are performed in both pure and full QCD and in both the confinement and deconfinement phase. We find an enhanced probability for monopoles inside the core of an instanton on gauge field average. This is independent of the topological charge definition used. For specific gauge field configurations we visualize the situation graphically. Moreover the correlation of monopole loops and instantons with the chiral condensate is investigated. Strong evidence is found that clusters of the quark condensate and topological objects coexist locally on individual configurations.     

Influence of the degree of long-range atomic order on parameters of the solid solution and the granular structure of the Pd3Fe alloy with superstructure L12

It has been established using X-ray structural analysis and scanning electron microscopy that the lattice parameter and total root-mean-square (rms) atomic displacements increase in the Pd₃Fe polycrystal-line alloy during the A1 → L1₂ phase transition and with an increase in the degree of long-range atomic order, while the microdistortions of the crystal lattice and the fraction of the Σ3 twin boundaries in the spectrum of special boundaries decrease; the latter leads to strengthening the texture.