Evaluating the topological charge density with the symmetricmulti-probing method

We evaluate the topological charge density of SU(3) gauge fields on a lattice by calculating the trace of the overlap Dirac matrix employing the symmetric multi-probing(SMP) method in 3 modes. Since the topological charge Q for a given lattice configuration must be an integer number, it is easy to estimate the systematic error(the deviation of Q to the nearest integer). The results demonstrate a high efficiency and accuracy in calculating the trace of the inverse of a large sparse matrix with locality by using the SMP sources when compared to using point sources.We also show the correlation between the errors and probing scheme parameter r_(min), as well as lattice volume N_L and lattice spacing a. It is found that the computational time for calculating the trace by employing the SMP sources is less dependent on N_L than by using point sources. Therefore, the SMP method is very suitable for calculations on large lattices.     

Topological susceptibility from overlap fermion

We numerically calculate the topological charge of the gauge configurations on a finite lattice by the fermionic method with overlap fermions. By using the lattice index theorem, we identify the index of the massless overlap fermion operator to the topological charge of the background gauge configuration. The resulting topological susceptibility χ is in good agreement with the anticipation made by Witten and Veneziano.     

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.     

Anomalies, gauge field topology, and the lattice

Motivated by the connection between gauge field topology and the axial anomaly in fermion currents, I suggest that the fourth power of the naive Dirac operator can provide a natural method to define a local lattice measure of topological charge. For smooth gauge fields this reduces to the usual topological density. For typical gauge field configurations in a numerical simulation, however, quantum fluctuations dominate, and the sum of this density over the system does not generally give an integer winding. On cooling with respect to the Wilson gauge action, instanton like structures do emerge. As cooling proceeds, these objects tend shrink and finally “fall through the lattice.” Modifying the action can block the shrinking at the expense of a loss of reflection positivity. The cooling procedure is highly sensitive to the details of the initial steps, suggesting that quantum fluctuations induce a small but fundamental ambiguity in the definition of topological susceptibility.     

On the ground state of Yang–Mills theory

We investigate the overlap of the ground state meson potential with sets of mesonic-trial wave functions corresponding to different gluonic distributions. We probe the transverse structure of the flux tube through the creation of non-uniform smearing profiles for the string of glue connecting two color sources in Wilson loop operator. The non-uniformly UV-regulated flux-tube operators are found to optimize the overlap with the ground state and display interesting features in the ground state overlap.     

Glueball spectrum from N_f=2 lattice QCD study on anisotropic lattices

The lowest-lying glueballs are investigated in lattice QCD using N_f = 2 clover Wilson fermions on anisotropic lattices. We simulate at two different and relatively heavy quark masses, corresponding to physical pion masses of mπ～938 MeV and 650 MeV. The quark mass dependence of the glueball masses has not been investigated in the present study. Only the gluonic operators built from Wilson loops are utilized in calculating the corresponding correlation functions. In the tensor channel, we obtain the ground state mass to be 2.363(39) GeV and 2.384(67)GeV at mπ～938 MeV and 650 MeV, respectively. In the pseudoscalar channel, when using the gluonic operator whose continuum limit has the form of ∈_ijkTrB_iD_jB_k, we obtain the ground state mass to be 2.573(55) GeV and 2.585(65) GeV at the two pion masses. These results are compatible with the corresponding results in the quenched approximation. In contrast, if we use the topological charge density as field operators for the pseudoscalar, the masses of the lowest state are much lighter(around 1 GeV) and compatible with the expected masses of the flavor singlet qq meson. This indicates that the operator ∈ijk TrBiDjBk and the topological charge density couple rather differently to the glueball states and qq mesons. The observation of the light flavor singlet pseudoscalar meson can be viewed as the manifestation of effects of dynamical quarks. In the scalar channel, the ground state masses extracted from the correlation functions of gluonic operators are determined to be around 1.4-1.5 GeV, which is close to the ground state masses from the correlation functions of the quark bilinear operators. In all cases, the mixing between glueballs and conventional mesons remains to be further clarified in the future.     

Gauge fixing, families index theory, and topological features of the space of lattice gauge fields

The families index theory for the overlap lattice Dirac operator is applied to derive topological features of the space of SU(N) lattice gauge fields on the 4-torus: the topological sectors, specified by the fermionic topological charge, are shown to contain noncontractible even-dimensional spheres when N3, and noncontractible circles in the N=2 case. We describe how certain obstructions to the existence of gauge fixings without the Gribov problem in the continuum setting correspond on the lattice to obstructions to the contractibility of these spheres and circles. We also point out a canonical connection on the space of lattice gauge fields with monopole-like singularities associated with the spheres.     

Topological susceptibility in lattice QCD and perturbation theory

We consider the definition of topological susceptibility suggested by the anomaloys U_A(1) Ward identify in lattice QCD with Wilson fermions and show that, in the limit of zero renormalized quark mass, its perturbative expansion is zero to all orders. This definition is thus suitable for Monte Carlo simulations.     

Non-renormalization of induced charges and constraints on strongly coupled theories

It is shown that global fermionic charges induced in vacuum by slowly varying, topologically non-trivial background scalar fields are not renormalized provided that expansion in momenta of background fields is valid. This suggests that strongly coupled theories obey induced charge matching conditions which are analogous, but generally not equivalent, to 't Hooft anomaly matching conditions. We give a few examples of induced charge matching. In particular, the corresponding constraints in softly broken supersymmetric QCD suggest non-trivial low-energy mass pattern, in full accord with the results of direct analyses.     

Monopoles in the presence of the Chern–Simons term via the Julia–Toulouse approach

We study QED₃ with magnetic-like defects using the Julia–Toulouse condensation mechanism (JTM) introduced in [F. Quevedo, C.A. Trugenberger, Nucl. Phys. B 501 (1997) 143, arXiv:hep-th/9604196]. By a careful treatment of the symmetries we suggest a geometrical interpretation for distinct debatable issues in the MCS-monopole system: (i) the induction of the non-conserved electric current together with the Chern–Simons term (CS), (ii) the deconfinement transition and, (iii) the computation of the fermionic determinant in the presence of Dirac string singularities. The JTM leads to proper interpretation of the non-conserved current as originating from Dirac brane symmetry breaking. The mechanism behind this symmetry breaking is clarified. The physical origin of the deconfinement transition becomes evident in the low energy effective theory induced by the JTM. The proper procedure to compute the fermionic determinant in the presence of Dirac branes will be presented. A byproduct of this approach is the possible appearance of statistical transmutation and the clarification for the different quantization rules for the topological mass.     

Axial Anomaly and Topological Charge in Lattice Gauge Theory with Overlap Dirac Operator

An explicit, detailed evaluation of the classical continuum limit of the axial anomaly and index density of the overlap Dirac operator is carried out in the infinite volume setting and in a certain finite volume setting where the continuum limit involves an infinite volume limit. Our approach is based on a novel power series expansion of the overlap Dirac operator. The correct continuum expression is reproduced when the parameter m₀ is in the physical region 0<m₀<2. This is established for a broad range of continuum gauge fields. An analogous result for the fermionic topological charge, given by the index of the overlap Dirac operator, is then established for a class of topologically nontrivial fields in the aforementioned finite volume setting. Problematic issues concerning the index in the infinite volume setting are also discussed.     

Induced vacuum quantum numbers in 2 + 1 dimensions

We calculate the induced vacuum fermionic charge and angular momentum in 2 + 1 dimensions around an abelian magnetic flux tube configuration, using a space compactification technique. It is found that the charge and the total angular momentum are topological invariants and depend on the total magnetic flux, while the fermionic angular momentum depends on the local features of the gauge field configuration and vanishes in the limit of a tube with diameter large compared with the Compton wavelength of the fermions.     

Topology of dynamical lattice configurations including results from dynamical overlap fermions

We investigate how the topological charge density in lattice QCD simulations is affected by violations of chiral symmetry caused by the fermion action. To this end we compare lattice configurations generated with a number of different actions including first configurations generated with exact dynamical overlap quarks. We visualize the topological profiles after mild smearing. In the topological charge correlator we measure the size of the positive core, which is known to shrink to zero extension in the continuum limit. To leading order we find the core size to scale linearly with the lattice spacing with the same coefficient for all actions, even including quenched simulations. In the subleading term the different actions vary over a range of about 10%. Our findings suggest that non-chiral lattice actions at current lattice spacings do not differ much for observables related to topology, both among themselves and compared to overlap fermions.     

Fermionic vacuum polarization in compactified cosmic string spacetime

We investigate the fermionic condensate and the vacuum expectation value (VEV) of the energy-momentum tensor for a charged massive fermionic field in the geometry of a cosmic string compactified along its axis. In addition, we assume the presence of two types of magnetic fluxes: a flux running along the cosmic string and another enclosed by the compact dimension. These fluxes give rise to Aharanov–Bohm-like effects on the VEVs. The VEVs are decomposed into two parts corresponding to the geometry of a straight cosmic string without compactification plus a topological part induced by the compactification of the string axis. Both contributions are even periodic functions of the magnetic fluxes with period equal to the flux quantum. The vacuum energy density is equal to the radial stress for the parts corresponding to the straight cosmic string and the topological one. Moreover, the axial stress is equal to the energy density for the parts corresponding to the straight cosmic string; however, for massive fermionic fields this does not occur for the topological contributions. With respect to the dependence on the magnetic fluxes, both the fermionic condensate and the vacuum energy density, can be either positive or negative. Moreover, for points near the string, the main contribution to the VEVs comes from the straight cosmic string part, whereas at large distances the topological ones dominate. In addition to the local characteristics of the vacuum state, we also evaluate the part in the topological Casimir energy induced by the string.     

Evidence for fine tuning of fermionic modes in lattice gluodynamics

We consider properties of zero and near-zero fermionic modes in lattice gluodynamics. The modes are known to be sensitive to the topology of the underlying gluonic fields in the quantum vacuum state of the gluodynamics. We find evidence that these modes are fine-tuned; that is, they exhibit sensitivity to both physical (one can say, hadronic) scale and to the ultraviolet cutoff. Namely, the density of the states is in physical units, while the localization volume of the modes tends to zero in physical units with the lattice spacing tending to zero. We briefly discuss the possible theoretical implications and also include some general, review-type remarks.     

Disordered d-wave superconductors with interactions

We study the localization properties of disordered d-wave superconductors by means of the fermionic replica trick method. We derive the effective non-linear σ-model describing the diffusive modes related to spin transport which we analyze by the Wilson–Polyakov renormalization group. A lot of different symmetry classes are considered within the same framework. According to the presence or the absence of certain symmetries, we provide a detailed classification for the behavior of some physical quantities, like the density of states, the spin and the quasiparticle charge conductivities. Following the original Finkel'stein approach, we finally extend the effective functional method to include residual quasiparticle interactions, at all orders in the scattering amplitudes. We consider both the superconducting and the normal phase, with and without chiral symmetry, which occurs in the so-called two-sublattice models.     

Glueballs and the superfluid phase of Two-Color QCD

We present the first results on scalar glueballs in cold, dense matter using lattice simulations of two-color QCD. The simulations are carried out on a 6³×12 lattice and use a standard hybrid molecular dynamics algorithm for staggered fermions for two values of quark mass. The glueball correlators are evaluated via a multi-step smearing procedure. The amplitude of the glueball correlator peaks in correspondence with the zero temperature chiral transition, μ _c=m _π /2, and the propagators change in a significant way in the superfluid phase, while the Polyakov loop is nearly insensitive to the transition. Standard analysis suggest that lowest mass in the 0⁺⁺ gluonic channel decreases in the superfluid phase, but these observations need to be confirmed on larger and more elongated lattices. These results indicate that a non-zero density induces non-trivial modifications of the gluonic medium.     

Degeneracy of the vacuum state according to chirality in the sigma-model with massless fermions

The degeneracy of the vacuum according to chirality is proved. It is shown that the local source of the fermionic field leads to a change of the chiral charge density. This signifies screening of the chiral charge and, possibly, confinement. Both effects are due to topological fluctuations of the sigma-field.St. Petersburg Higher Military Engineering College of Communications. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 77–80, November, 1993.     

基于超材料与电阻型频率选择表面的薄型宽频带吸波体的设计

设计了三种类型吸波体, 分别为基于正方形金属贴片(square metal patch, SMP) 结构超材料吸波体、 电阻型频率选择表面(Resistance Frequency Selective Surface, RFSS) 吸波体和SMP与RFSS的复合结构吸波体. 采用FDTD算法分别对这三种类型吸波体的电磁波吸收特性进行数值模拟分析. 模拟得到的结果表明: 在整个2-30 GHz频率范围内, SMP吸波体, 通过几何参数的设计可以实现多频窄带强吸收; RFSS吸波体, 通过方块电阻的设计可以实现高频宽带强吸收, 但强吸收的带宽有限; SMP与RFSS的复合结构吸波体, 在3-25 GHz之间吸收率大于90%以上, 且宽频范围内与自由空间具有较好的阻抗匹配特性.     

Wilson fermions and the topological charge on the lattice

We investigate the realization on the lattice of the relation between the chiral properties of the fermions and the topological properties of the gauge field. A lattice definition of the topological charge density via the U(1) Adler-Bardeen anomaly is analysed with the help of given configurations of nontrivial topology and for 2-dimensional quenched QED.