The Spatial String Tension and Dimensional Reduction in QCD
M. Cheng, S. Datta, J. van der Heide, K. Huebner, F. Karsch, O. Kaczmarek, E. Laermann, J. Liddle, R. D. Mawhinney, C. Miao, P. Petreczky, K. Petrov, C. Schmidt… 展开作者
M. Cheng, S. Datta, J. van der Heide, K. Huebner, F. Karsch, O. Kaczmarek, E. Laermann, J. Liddle, R. D. Mawhinney, C. Miao, P. Petreczky, K. Petrov, C. Schmidt, W. Soeldner, T. Umeda
We calculate the spatial string tension in (2+1) flavor QCD with physical strange quark mass and almost physical light quark masses using lattices with temporal extent N_tau=4,6 and 8. We compare our results on the spatial string tension with predictions of dimensionally reduced QCD. This suggests that also in the presence of light dynamical quarks dimensional reduction works well down to temperatures 1.5T_c.
We study the string tension as a function of temperature, fitting the SU(3) lattice QCD finite temperature free energy potentials computed by the Bielefeld group. We compare the string tension points with order parameter curves of ferromagnets, superconductors or string models, all related to confinement. We also compare the SU(3) string tension with the one of SU(2) Lattice QCD. With the curve providing the best fit to the finite temperature string tensions, the spontaneous magnetization curve, we then show how to include finite temperature, in the state of the art confining and chiral invari…
We investigate Abelian and monopole contributions to spatial string tension in the deconfined phase of finite temperature SU(2) gauge theory without imposing any gauge fixing conditions. Lattice calculations of non-Abelian and Abelian spatial string tensions from the Wilson action at gauge coupling $β=2.74$ and lattice volume $24^3\times{N_t}$ $(N_{t}=\left\{ 24,8,6,4,2)\right\}$ show that these string tensions agree with each other within error bars at any adopted value of $N_t$, which implies Abelian dominance. From measurements of non-Abelian, Abelian, and monopole forces that arise from th…
The critical curve of string tension as a function of the temperature is computed in SU(3) Lattice QCD. We present the results for the string tension utilizing a pair of Polyakov loop and antiloop, with two different techniques. We compare the colour averaged loop-antiloop which is gauge invariant but is only adequate to study the string tension, and the colour singlet loop-antiloop using the Landau gauge fixing which also enables to compute the coulomb part of the free energy.
In pure SU(N) gauge theory in four dimensions, we determine the string tension at large N from smeared rectangular Wilson loops on the lattice. We learn how well loops of sizes barely on the strong-coupling side of the large-N transition in their eigenvalue distribution can be described by effective string theory.
We consider whether the 1/N corrections to k-string tensions must begin at order 1/N^2, as in the Sine Law, or whether odd powers of 1/N, as in Casimir Scaling, are also acceptable. The issue is important because different models of confinement differ in their predictions for the representation-dependence of k-string tensions, and corrections involving odd powers of 1/N would seem to be ruled out by the large-N expansion. We show, however, that k-string tensions may, in fact, have leading 1/N corrections, and consistency with the large-N expansion, in the open string sector, is achieved by an …
We calculate the low-lying glueball spectrum and various string tensions in SU(N) lattice gauge theories in 2+1 dimensions, and extrapolate the results to the continuum limit. We do so for for the range N=2 to N=16 so as to control the N-dependence with a useful precision. We observe a number of striking near-degeneracies in the various J^PC sectors of the glueball spectrum, in particular between C=+ and C=- states. We calculate the string tensions of flux tubes in a number of representations, and provide evidence that the leading correction to the N-dependence of the k-string tensions varies …
The Interface Tension in Quenched QCD at the Critical Temperature
我们给出了淬火QCD的约束-解除约束界面张力$α_{cd}$的结果。它们是通过将Binder直方图方法应用于尺寸为$L^2\times L_z\times L_t$（对于$L_t=2$）和尺寸为$L=8,10,12\mbox{ and }14$（对于$L=8$）和尺寸为$L_z=30$（对于$L_z=3L$）的晶格而获得的。使用的multicanonical算法和圆柱形的几何形状已被证明是至关重要的数值研究。
We compute, via numerical simulations, the non-perturbative Coulomb potential of pure SU(3) gauge theory in Coulomb gauge. We find that that the Coulomb potential scales nicely in accordance with asymptotic freedom, that the Coulomb potential is linear in the infrared, and that the Coulomb string tension is about four times larger than the asymptotic string tension. We explain how it is possible that the asymptotic string tension can be lower than the Coulomb string tension by a factor of four.
We numerically compute the spatial string tension in the deconfined phase of three dimensional QCD in the large N limit. Our results clearly show that the string tension grows linearly with temperature.
Global string networks may be relevant in axion production in the early Universe, as well as other cosmological scenarios. Such networks contain a large hierarchy of scales between the string core scale and the Hubble scale, log(f/H) around 70, which influences the network dynamics by giving the strings large tensions T = pi f^2 log(f/H). We present a new numerical approach to simulate such global string networks, capturing the tension without an exponentially large lattice.
We consider three-dimensional SU(N) gauge theories with massless Dirac or Majorana fermions in the adjoint representation. We use the Eguchi-Kawai volume reduction to two-dimensions to calculate the tension sigma_k of the k-string in such theories. Under some assumptions whose validity we discuss, we derive the previously conjectured sine formula, sigma_k ~ N sin pi k/N.
Continuum reduction and Monte Carlo simulation are used to calculate the heavy quark potential and the string tension in large N Yang-Mills theory in four dimensions. The potential is calculated out to a separation of nine lattice units on a lattice with extent six in each direction.
We investigate the properties of global cosmic string networks as a function of the ratio of string tension to Goldstone-field coupling, and as a function of the Hubble damping strength. Our results show unambiguously that the string density is sensitive to this ratio. We also find that existing semi-analytical (one-scale) models must be missing some important aspect of the network dynamics. Our results point the way towards improving such models.
Using smeared Creutz ratios we extract the string tension for SU(N) pure gauge theory and $N$=3,4,5,6,8. We employ these results to extrapolate to large N. The same methodology is applied to the single-site Twisted Eguchi Kawai model. The corresponding string tension matches perfectly within errors with the extrapolated one, providing strong evidence in favour of the twisted reduction framework. Interesting results are also obtained on the behaviour of Creutz ratios for large sizes.
In the low temperature confining phase of QCD or QCD-like theories it is challenging to capture the temperature dependence of observables through AdS/CFT. Using the blackfold approach we compute the quark-antiquark linear static potential in the low temperature confining phase, taking into account the thermal excitations of the string. We find the explicit temperature dependence of the string tension and notice that, as naturally expected, tension decreases as temperature increases. We have also generalized the blackfold approach for the computation of the Wilson loops, making it directly appl…
Recently, we proposed a new method to extract the string tension from 4-dimensionally smeared Wilson loops. In this talk, we first show that the results obtained using this smearing method are identical to those obtained by Wilson flow, once the time step is sufficiently small. We then demonstrate the practical advantage of our method by applying it to the calculation of string tension in SU(3) Yang-Mills theory.
From continuum studies it is known that the Coulomb string tension $σ_C$ gives an upper bound for the physical (Wilson) string tension $σ_W$ [D. Zwanziger, Phys. Rev. Lett. 90, 102001 (2003)]. How does however such relationship translate to the lattice? In this paper we give evidence that there, while the two string tensions are related at zero temperature, they decouple at finite temperature. More precisely, we show that on the lattice the Coulomb gauge confinement scenario is always tied to the spatial string tension, which is known to survive the deconfinement phase transition and to cause …
We explore the performance of CUDA in performing Landau gauge fixing in Lattice QCD, using the steepest descent method with Fourier acceleration. The code performance was tested in a Tesla C2070, Fermi architecture. We also present a study of the string tension at finite temperature in the confined phase. The string tension is extracted from the color averaged free energy and from the color singlet using Landau gauge fixing.
SU(N) gauge theories, extended with adjoint fermions having periodic boundary conditions, are confining at high temperature for sufficiently light fermion mass $m$. In the high temperature confining region, the one-loop effective potential for Polyakov loops has a Z(N)-symmetric confining minimum. String tensions associated with Polyakov loops are calculable in perturbation theory, and display a novel scaling behavior in which higher representations have smaller string tensions than the fundamental representation. In the magnetic sector, the Polyakov loop plays a role similar to a Higgs field,…
We improve upon recent calculations of the low-lying `glueball' spectra of SO(3) and SO(4) lattice gauge theories in 2+1 dimensions, and compare the resulting continuum extrapolations with SU(2). We find that these are reasonably consistent, as are the SU(2) and SO(4) string tensions when these are corrected for the differing representations of the flux. All this indicates that the different global properties of these groups do not play a significant role in the low-lying physics.
We address the question of whether the large-N expansion in pure SU(N) gauge theories requires that k-string tensions must have a power series expansion in 1/N^2, as in the sine law, or whether 1/N contributions are also allowable, as in Casimir scaling. We find that k-string tensions may, in fact, have 1/N corrections, and consistency with the large-N expansion in the open-string sector depends crucially on an exact cancellation, which we will prove, among terms involving odd powers of 1/N in particular combinations of Wilson loops. It is shown how these cancellations are fulfilled, and consi…
