Numerical analysis of the twisted Eguchi-Kawai model in four dimensions

We perform a high statistics Monte Carlo calculation of the string tension in the twisted SU(N) Eguchi-Kawai model for N=36 and N=64. The string tension, calculated from Wilson loops not larger than 3 × 3, clearly shows the renormalization group scaling behaviour.     

Generalized roughening transition and its effect on the string tension

The well-understood roughening transition of an interface in the d = 3 Ising model implies an essential singularity in the string tension of the dual Z₂ gauge model. The roughening transition corresponds to the delocalization of the string due to strong long-wavelength fluctuations, and this reformulation can be generalized to other gauge groups and to d = 4 also. It is not a deconfining transition - it is expected to occur deep in the confining region - but its presence would raise serious questions about the continuation of strong coupling expansions of the tension beyond this point. In this paper predictions on the roughening transition are confronted with the available information on the string tension for different gauge groups in three dimensions.     

Numerical study of Langevin equation in twisted Eguchi-Kawai model

The Langevin equation at the group manifolds is derived and investigated for the twisted Eguchi-Kawai model The numerical results for the string tension for various values of N are combined with the known Monte Carlo results to give an improved value of the string tension. The distribution of eigenvalues of Wilson loop matrices are also studied.     

SU(2) Lattice gauge theory in (2+1)D

Cluster expansion methods are applied to theSU(2) lattice gauge model in (2+1) dimensions. Strong-coupling series are calculated for the vacuum energy per site, the axial string tension, and the scalar mass gap; while ELCE approximants are used to estimate the string tension beyond its roughening transition. The simple scaling behaviour expected of this super-renormalizable theory is clearly seen, and we estimate that in the continuum limit the string tension σ～(0.14±0.01)g ⁴, while the mass gapM _s ～(2.2±0.25)g ². More accurate Monte Carlo simulations are needed to check the universality between the Hamiltonian and Euclidean versions of this model.     

Linked cluster expansions for U(1) lattice gauge theory in 2 + 1 and 3 + 1 dimensions

Compact U(1) lattice gauge theory is studied in 2 + 1 and 3 + 1 dimensions using strong coupling series expansions and the recently proposed exact linled cluster expansion alborithm Results for the vacuum energy, specific heat and axial string tension in 2 + 1 dimensions are in agreement with previous finite lattice estimates. In 3 + 1 dimensions, we present new strong coupling series results (order g^?40) which together with the ELCE estimates show evidence of a continuous phase transition at x = 1/g⁴ = 0.72 ± 0.08. The associated critical index for the vanishing string tension is μ = 0.65 ± 0.12. The axial string tension in D = 3 + 1 appears to undergo a non-deconfining roughening transition at smaller x (0.56 ± 0.07).     

On the roughening transition in abelian lattice gauge theories

We study the width of the confining string between static quarks in abelian lattice gauge theories using strong coupling expansions. We consider gauge groups Z_n and U(1) in 3 and 4 dimensions. This extends previous work with Lüscher, where SU(2) and Z₂ were studied. In ν = 3 dimensions we find evidence for a roughening transition. It is characterized by a divergence of the string width for an infinitely far separated quark-antiquark pair, while the string tension remains non-zero. In ν = 4 dimensions for the abelian groups we do not have evidence for a roughening transition away from a phase transition.     

Variational calculations in the gluon sector of the lattice QCD

The partition function ofd dimensional systems is estimated with the help of a variational Ansatz in terms of quasi-(d-1)-dimensional systems. The internal energy and the string tension derived in this framework agree reasonably with the Monte Carlo data.     

Wilson loops on 324 lattices and theSU(3) potential

Wilson loops are calculated on 32⁴ lattices in the coupling regime 6/g ²=6.3–6.9. Determination of the string tension from these loops with a method based on string model calculations shows a string tension that does not seem to scale. This is probably due to the amount of statistics. It points to difficulties in obtaining accurate physical results for coupling values above 6.6. Suggestions to improve this situation are made.     

Portraits of the flux tube in QED3: A Monte Carlo simulation with external sources

We determine numerically, and display graphically, the electromagnetic energy distribution due to static sources in compact QED₃. Using the polymer formulation of the functional integral, Monte Carlo simulations are performed with external sources included in the lattice action. Both the Wilson and Villain forms of the action are studied, and the string tension is determined in a small range of weak couplings. For the Villain action, our values for the string tension σ are in agreement with Polyakov's formula. For the Wilson action, we are able to detect a string tension in a range of weak couplings 2.1 ? β ? 2.3 below the weak-to-strong coupling cross-over point. In the same range, standard Monte Carlo results for up to 8 × 8 Wilson loops are consistent with ordinary perturation theory (no confinement). A possible explanation of this discrepancy is discussed, and it is suggested that the standard (source-free) Monte Carlo might miss configurations which are important for flux-tube formation.     

Plane waves in effective field theories of superstrings

Exact plane wave solutions of d = 10, N = 1 Einstein-Yang-Mills supergravity theory are presented and their possible modifications in superstring effective theories are examined. It is found that the solutions are not affected by any of the known heterotic string corrections. It is argued that plane waves satisfy the effective field equations of the heterotic string theory in all powers of the string tension parameter α′, possibly after including a totally antisymmetric torsion field and reinterpreting the constants. Similar remarks also apply for type I superstrings. Further properties of the solutions are discussed.     

Vacuum background fields in QCD as a source of confinement

Quarks and gluons in the vacuum background field with a finite correlation length d are shown to be linearly confined inside white states. The string tension for an arbitrary representation of SU(N) is obtained in terms of d and the gluon condensate and agrees with numerical data and large N behaviour. The QCD string picture is shown to emerge asymptotically at large euclidean distances.     

The string tension of compact U(1) four-dimensional lattice gauge theory

Monte Carlo simulations of the string tension are calculated for four-dimensional U(1) gauge theory on a 6⁴ lattice. The string tension follows the result -1n(β/2) in the high temperature region and is zero for β > β_c, where β_c is the critical inverse temperature.     

Hadron potentials within the gauge/string correspondence

It is known, since the 70s, that the large N 't Hooft limit of gauge theories is related to string theories. In 1998, J. M. Maldacena identified precisely such a relation: the so-called AdS/CFT correspondence which speculates a duality between a large N strongly-coupled supersymmetric and conformal Yang-Mills theory in four dimensions and a weakly-coupled string theory defined in a five-dimensional anti-de Sitter AdS₅ space-time. This review aims at introducing concepts and methods used to derive, in the framework of the gauge/string correspondence, the interaction potentials of mesons and baryons at zero and finite temperature. The dual string configurations associated with the different kinds of hadrons are described and their behaviours at short and large distances are understood. Although the application of Maldacena's AdS/CFT conjecture to QCD is not straightforward, QCD being neither supersymmetric nor conformal, the AdS/QCD correspondence approach attempts to identify the dual theory of QCD. Especially, the study of heavy quark-antiquark bound-states leads to establish general dual criteria for the confinement.     

U(3) four-dimensional lattice gauge theory and Monte Carlo calculations

Monte Carlo results for the pure U(3) lattice gauge theory on a 6⁴ lattice are reported. Wilson loops and the string tension are presented. The first-order phase transition in U(3) is reflected quite clearly in a discontinuity in the string tension at β = β_c. The U(1) factor of U(3) is extracted using the determinant of the Wilson loops. As expected, the U(1) component appears to deconfine at the phase transition..     

弦线驻波实验装置改进

本文对典型弦线驻波实验中数据不够准确、驻波不稳定及实验可重复性差等现象进行了分析,明确其根本原因在于实验装置设计方案存在缺陷.提出了实验装置改进方案,一是引入拉力传感器取代狭缝刀口和悬挂重物,改变反射波的形成机理,并以弦线张力直接测量取代砝码重力间接计算;二是引入机械结构微调弦线长度以改变弦线张力和弦线上驻波波长.实验结果证明,改进后的实验装置能明显改善上述问题,该装置还可实施研究驻波规律的多个实验方案。     

Vortex free energy and string tension at strong and intermediate coupling

We present results of high temperature expansions up to order g^?24 for the vortex free energy respectively string tension in pure lattice gauge theories with gauge groups SU(2) and Z₂ in 3 and 4 dimensions. For SU(2) in 4 dimensions the result is compared with Monte Carlo calculations of Creutz and is in good agreement. An intermediate coupling region is seen, where the string tension smoothly interpolates between strong coupling and weak coupling behaviour.     

Spectrum of heavy-light mesons in the QCD string picture

We describe in detail predictions of the QCD string approach for the masses of the heavy—light D, D _s , B, and B _s mesons, including orbitally and radially excited states. We discuss the role of the proper dynamics of the QCD string in the formation of the spectrum of the heavy—light mesons, with quark self-energy corrections calculated self-consistently in the same picture. We give our predictions in terms of the current quark masses; the string tension—the only dimensional parameter describing the interquark interaction; and the strong coupling constant, which differs for the fine and the hyperfine interactions. The results are compared with the predictions of other models and with the experimental and lattice results.     

Weak coupling perturbative calculations of the Wilson loop in lattice gauge theory

Weak coupling perturbative calculations of the Wilson loop in lattice gauge theory are carried out numerically up to order g⁴. Comparison of the results with those of the Monte Carlo calculations shows that there exists a non-perturbative contribution of an essential singularity type which may be identified as the string tension.     

Scaling in lattice QCD: Glueball masses and string tension

We study the scaling behaviour of lattice quantum chromodynamics by comparing the β dependence of the string tension and the 0⁺⁺ glueball mass. We use a source method at β=5.7, β=5.9 and β=6.1, on lattices from 9³· 24 to 16³· 32. Assuming a string tension of about (420 MeV)², the lattice spacing ranges from 0.16 to 0.08 fm. In order to separate finite volume from scaling violation effects we have compared data from lattices having approximately the same overall physical size at the different values of β. We find deviations from scaling to be very small.     

Physical mechanism of the (tri)critical point generation

We discuss some ideas resulting from a phenomenological relation recently declared between the tension of string connecting the static quark-antiquark pair and surface tension of corresponding cylindrical bag. This relation analysis leads to the temperature of vanishing surface tension coefficient of the QGP bags at zero baryonic charge density as T _?? = 152.9 ± 4.5 MeV. We develop the view point that this temperature value is not a fortuitous coincidence with the temperature of (partial) chiral symmetry restoration as seen in the lattice QCD simulations. Besides, we argue that T _?? defines the QCD (tri)critical endpoint temperature and claim that a negative value of surface tension coefficient recently discovered is not a sole result but is quite familiar for ordinary liquids at the supercritical temperatures.