Graphene wormholes: A condensed matter illustration of Dirac fermions in curved space

We study the properties of graphene wormholes in which a short nanotube acts as a bridge between two graphene sheets, where the honeycomb carbon lattice is curved from the presence of 12 heptagonal defects. By taking the nanotube bridge with very small length compared to the radius, we develop an effective theory of Dirac fermions to account for the low-energy electronic properties of the wormholes in the continuum limit, where the frustration induced by the heptagonal defects is mimicked by a line of fictitious gauge flux attached to each of them. We find in particular that, when the effective gauge flux from the topological defects becomes maximal, the zero-energy modes of the Dirac equation can be arranged into two triplets, that can be thought as the counterpart of the two triplets of zero modes that arise in the dual instance of the continuum limit of large spherical fullerenes. We further investigate the graphene wormhole spectra by performing a numerical diagonalization of tight-binding Hamiltonians for very large lattices realizing the wormhole geometry. The correspondence between the number of localized electronic states observed in the numerical approach and the effective gauge flux predicted in the continuum limit shows that graphene wormholes can be consistently described by an effective theory of two Dirac fermion fields in the curved geometry of the wormhole, opening the possibility of using real samples of the carbon material as a playground to experiment with the interaction between the background curvature and the Dirac fields.     

The sign factor of the three-dimensional Ising model and the quantum fermionic string

The sign factor ensuring the cancellation of self-intersecting two-dimensional surfaces in the partition function of the three-dimensional Ising model is defined. The possible equivalence of the continuum limit of the three-dimensional Ising gauge model to the Dirac action induced on two-dimensional surfaces is pointed out.     

Nonanalyticity in scale in the planar limit of QCD

Using methods of numerical lattice gauge theory we show that, in the limit of a large number of colors, properly regularized Wilson loops have an eigenvalue distribution which changes nonanalytically as the overall size of the loop is increased. This establishes a large-N phase transition in continuum planar gauge theory, a fact whose precise implications remain to be worked out.     

Wave processes in elastic-viscoplastic media with dislocations

The mechanisms of plane harmonic wave propagation in homogeneous and interfaced elastic-viscoplastic media are considered using the field theory of defects with kinematic identities of a dislocation-containing elastic continuum and dynamic equations of the gauge theory of dislocations. The reflection and refraction coefficients were determined for displacement waves and defect field waves with the defect field characterized by the dislocation density tensor and flux density tensor. The dependence of the coefficients on the parameters of the interfaced media is analyzed.     

Calculation of Vacuum Wavefunction and Mass .Gap from Improved (2+l)-Dimensional SU(2) Lattice Gauge Field Hamiltonian

The truncated eigenvalue equation of SU(N) lattice gauge theory is studied by using improved lattice gauge Hamiltonian with a proper truncation scheme that preserves the continuum limit. The calculations of vacuum state wavefunction and glueball mass of (2+1)-dimensional SU(2) theory up to third order are carried out, the results show the improvement of scaling behavior in deep weak coupling region.     

Analogies in electronic properties of graphene wormhole and perturbed nanocylinder

The electronic properties of the wormhole and the perturbed nanocylinder wereinvestigated using two different methods: the continuum gauge field-theory model thatdeals with the continuum approximation of the surface and the Haydock recursion methodthat transforms the surface into a simplier structure and deals with the nearest-neighborinteractions. Furthermore, the changes of the electronic properties were investigated forthe case of enclosing the appropriate structure, and possible substitutes for the encloserwere derived. Finally, the character of the electron flux through the perturbed wormholewas predicted from the model based on the multiwalled nanotubes. The effect of the“graphene blackhole” is introduced.     

Summations over equilaterally triangulated surfaces and the critical string measure

We propose a new approach to the summation over dynamically triangulated Riemann surfaces which does not rely on properties of the potential in a matrix model. Instead, we formulate a purely algebraic discretization of critical string path integral. This is combined with a technique which assigns to each equilateral triangulation of a two-dimensional surface a Riemann surface defined over a certain finite extension of the field of rational numbers, i.e. an arthmetic surface. Thus we establish a new formulation in which the sum over randomly triangulated surfaces defines an invariant measure on the moduli space of arithmetic surfaces. It is shown that because of this it is far from obvious that this measure for large genera approximates the measure defined by the continuum theory, i.e. Liouville theory or critical string theory. In low genus this subtlety does not exist. In the case of critical string theory we explicity compute the volume of the moduli space of arithmetic surfaces in terms of the modular height function and show that for low genus it approximates correctly the continuum measure. We also discuss a continuum limit which bears some resemblance with a double scaling limit in matrix models.This work was supported in part by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC03-76SF00098Supported in part by NSF grant PHY85-15857     

Berry phase in magnetic superconductors

In magnetic systems, electronic bands often acquire nontrivial topological structure characterized by gauge flux distribution in momentum k space. It sometimes follows that the phase of the wave functions cannot be defined uniquely over the whole Brillouin zone. In this Letter, we develop a theory of superconductivity in the presence of this gauge flux both in two- and three-dimensional systems. It is found that the superconducting gap has "nodes" as a function of k where the Fermi surface is penetrated by a gauge string.     

Size dependent surface energy of nanoplates: Molecular dynamics and nanoscale continuum theory correlations

A nanoscale gradient continuum theory along with molecular dynamics simulations are employed to investigate the size-dependent surface energy of nanoplates. Molecular dynamics simulations reveal that upon nanoplate thickness reduction, the redistribution of surface energy density along thickness direction causes the decrease of the surface energy of nanoplate free surfaces. Via introducing a calibration benchmark, the length scale model parameter of the gradient continuum theory is methodically determined. The calibrated continuum theory is shown to well predict the size-dependent surface energy and the associated redistribution of surface energy density within nanoplates.     

Isospin breaking of the narrow charmonium state of Belle at 3872 MeV as a deuson

We investigate the continuum limit of a compact formulation of the lattice U(1) gauge theory in 4 dimensions using a nonperturbative gauge-fixed regularization. We find clear evidence of a continuous phase transition in the pure gauge theory for all values of the gauge coupling (with gauge symmetry restored). When probed with quenched staggered fermions with U(1) charge, the theory clearly has a chiral transition for large gauge couplings. We identify the only possible region in the parameter space where a continuum limit with nonperturbative physics may appear.     

Metric-torsion gauge theory of continuum line defects

Basic points underlying the geometrization of continuum defects are discussed. Following an analogy with gravitational gauge theories, a metric-torsion gauge theory of continuum line defects is developed. Gauge-invariant action integrals are constructed and their equations of motion are obtained. A Lagrangian containing curvature terms up to second power has constant-curvature solutions. In linear approximation these solutions correspond to line defects which form closed loops separately.     

THE VARIATIONAL CALCULATION OF MASS GAP IN 2+1 DIMENSIONAL SU(2) LGT

A variational calculation of the mass gap in 2+1 dimensional SU(2) lattice gauge theory by using a Hamiltonian which possesses exact ground state and correct continuum limit is made.In the range 1.3≤1/g²≤7,a good scaling behaviour am=2.28g² is obtained,which is in agreement with weak-coupling perturbation theory and the results obtained by another Hamiltonian which does not possess correct continuum limit.     

Composite massless fermions in strongly coupled lattice gauge theories

We show that a class of strongly coupled lattice gauge theories with fermions in real representations of the gauge group do not have chiral symmetry breaking. The resulting spectrum of massless composite fermions satisfies 't Hooft's constraints if the model is naively extrapolated to the continuum limit. We argue that it is in fact the correct spectrum of the continuum gauge theory.     

Center vortex properties in the Laplace-center gauge of SU(2) Yang–Mills theory

Resorting to the the Laplace center gauge (LCG) and to the Maximal-center gauge (MCG), respectively, confining vortices are defined by center projection in either case. Vortex properties are investigated in the continuum limit of SU(2) lattice gauge theory. The vortex (area) density and the density of vortex crossing points are investigated. In the case of MCG, both densities are physical quantities in the continuum limit. By contrast, in the LCG the piercing as well as the crossing points lie dense in the continuum limit. In both cases, an approximate treatment by means of a weakly interacting vortex gas is not appropriate.     

Continuum limit of A Z2 lattice gauge theory

Phase diagrams of lattice gauge theories have in several cases lines of first-order transitions ending at points at which continuous (second-order) transitions take place. In the vicinity of this critical point, a continuum field theory may be defined. We have analyzed here a Z₂ gauge plus matter model (which has no formal continuum limit) and identified the critical point with a usual Ø⁴, globally Z₂ invariant, field theory. The analysis relies on a mean field functional formalism and on a loop-wise expansion around it, which is reviewed.     

Monte Carlo simulation of non-compact QCD with stochastic gauge fixing

A non-compact lattice model of quantum chromodynamics is studied numerically. Whereas in Wilson's lattice theory the basic variables are the elements of a compact Lie group, the present lattice model resembles the continuum theory in that the basic variables A are elements of the corresponding Lie algebra, a non-compact space. The lattice gauge invariance of Wilson's theory is lost. As in the continuum, the action is a quartic polynomial in A, and a stochastic gauge fixing mechanism - which is covariant in the continuum and avoids Faddeev-Popov ghosts and the Gribov ambiguity — is also transcribed to the lattice. It is shown that the model is self-compactifying, in the sense that the probability distribution is concentrated around a compact region of the hyperplane div A = 0 which is bounded by the Gribov horizon. The model is simulated numerically by a Monte Carlo method based on the random walk process. Measurements of Wilson loops, Polyakov loops and correlations of Polyakov loops are reported and analyzed. No evidence of confinement is found for the values of the parameters studied, even in the strong coupling regime.     

用改进的格点哈密顿量计算2+1维SU(3)胶球质量

应用改进的格点哈密顿量和保持连续极限的耦合集团展开方法计算了2+1维SU(3)0⁺和0^－胶球的质量.计算到三级近似,标度行为已经很好.与未改进的格点哈密顿量作的同样近似比较,改进的结果较快地进入标度区,而且标度性也较好.     

Electric/magnetic flux tube on the background of magnetic/electric field

It is argued that the phenomenon of a flux tube in quantum chromodynamics is closely connected with a spontaneously symmetry breakdown of gauge theory. It is shown that in the presence of a mass term in the SU(2) gauge theory the Nielsen‐Olesen equations describe the flux tube surrounded by an external field.