Anatomy of isolated monopole in Abelian projection of SU(2) lattice gauge theory

We study the structure of isolated static monopoles in the maximal Abelian projection of SU(2) lattice gluodynamics. Our estimation of the monopole radius is: R ^mon≈0.06 fm.     

Gluon condensate from SU(2) lattice gauge theory

Recent Monte Carlo results are analyzed in terms of an operator product expansion for Wilson loops of small size. The value of 〈α_sG_μν^aG_μν^a〉 is found to be consistent with previous phenomenological estimates.     

On the stochastic confinement in SU(2) lattice gauge theory

We extend the Olesen approach to confinement, originally proposed for SU(∞) gauge theory, to the SU(2) group. We perform Monte Carlo calculations of the spectral density, which describes the distribution of eigenvalues of the Wilson loop in the SU(2) lattice gauge theory (LGT), for square loops up to size 4 × 4. Our results indicate the onset of disorder in the 4-dimensional LGT so that at weak coupling confinement is due to non-abelian fluctuations of the gauge field. We describe the Monte Carlo data by formulae of the 2-dimensional LGT with some effective coupling constant. We formulate how this effective coupling constant should depend on the size of the loop in order that the Olesen hypothesis about the dimensional reduction (i.e. approximate reduction of the 4-dimensional LGT to the effective 2-dimensional LGT in the confinement region) would be held. Using the strong-coupling expansion where the Olesen hypothesis holds in fourteen orders, we perform quantitative estimates. The density of simple vortices up to size 4 × 4 is calculated. A connection between the definitions of spectral densities for the SU(∞) and SU(2) groups is considered. Explicit formulae for the spectral density in the 2-dimensional SU(2) LGT are derived.     

Universality in SU(2) lattice gauge theory

A method of resumming perturbation theory is used to re-analyze previous Monte Carlo data of Bhanot and Dashen. We find no inconsistency with universality. There appears to be a relatively large region where Monte Carlo studies can reliably be done.     

Thermal monopoles in the SU(2) gauge theory on a lattice

Color-magnetic thermal monopoles in SU(2) lattice gluodynamics with improved Simanzik action were studied. The density of the monopoles, the monopole chemical potential, the cluster susceptibility, and the cluster magnetization were studied. These results were compared with results that were reported elsewhere.     

Finite temperature SU(2) lattice gauge theory

We discuss SU(2) lattice gauge theories at non-zero temperature and prove several rigorous results including i) the absence of confinement for sufficiently high temperature in the pure gauge theory, and ii) the absence of spontaneous chiral symmetry breaking for sufficiently high temperature in the theory with massless fundamental representation fermions.     

SU (2) lattice gauge theory simulations on Fermi GPUs

In this work we explore the performance of CUDA in quenched lattice SU (2) simulations. CUDA, NVIDIA Compute Unified Device Architecture, is a hardware and software architecture developed by NVIDIA for computing on the GPU. We present an analysis and performance comparison between the GPU and CPU in single and double precision. Analyses with multiple GPUs and two different architectures (G200 and Fermi architectures) are also presented. In order to obtain a high performance, the code must be optimized for the GPU architecture, i.e., an implementation that exploits the memory hierarchy of the CUDA programming model.     

Monopole order parameter in SU(2) lattice gauge theory

We report the results of numerical calculations for the probability distribution of the values of the monopole creation operator Ф_mon in the maximal Abelian projection of SU(2) lattice gluodynamics. It turns out that at low temperature in the confinement phase the maximum of the distribution corresponds to a nonzero value of the field Ф_mon. This means that the effective potential has the form of a Higgs potential. Above the phase-transition point the minimum of the potential (the maximum of the distribution of the monopole creation operator) corresponds to a zero value of the monopole field Fmon. The results presented are a direct proof of the existence of a condensate of Abelian monopoles in the confinement phase of gluodynamics, and they confirm the hypothesis that the vacuum of gluodynamics is analogous to a dual superconductor. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 6, 392–397 (25 March 1996)     

PJLZ gauge-fixing approach in SU(2) lattice gauge theory

We study the SU(2) gauge theory with the interpolating gauge a la Parrinello-Jona-Lasinio-Zwanziger (PJLZ) with the gauge-fixing functional $F = \sum {_{x\mu } \frac{1}{2}} Tr\left( {U_{x\mu } \sigma _3 U_{x\mu }^\dag \sigma _3 } \right)$ . We find a strong indication of the nonanaliticity with respect to the interpolating parameter λ at c～0.8.     

Instantons and confinement in the SU(2) lattice gauge theory

We study the properties of gauge field configurations obtained by freezing the quantum fluctuations of the gauge fields on the lattice. The freezing process is subdivided into three regions: instanton-anti-instanton vacuum, the annihilation of (anti)instantons, and classical solutions. We obtain the distribution of instanton sizes, ϱ, and the distribution of interinstanton distances, R. The average value of the ratio R/ϱ is 2.3. The contribution of the multi-instanton configurations to the value of the string tension is 5%.     

On Nambu monopole dynamics in a SU(2) lattice Higgs model

It is shown that an SU(2) Higgs model on a lattice is equivalent to the Georgi-Glashow model in the limit of a small coupling constant between the Higgs and gauge fields. It can therefore be concluded that the transition between the confinement and symmetric phases in a 3 + 1 dimensional SU(2) Higgs model at finite temperature is accompanied by condensation of Nambu monopoles. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 9, 577–580 (10 November 1997)     

SU (2) lattice gauge theory and Monte Carlo calculations

Monte Carlo results for theSU (2) lattice gauge theory in four dimensions are presented. The string tension is measured with high statistics and also the mass of the perimeter term is determined. Wilson loop-plaquette correlations, which are related to roughening, are measured.     

Effective monopole potential for SU(2) lattice gluodynamics in the spatial maximal Abelian gauge

We investigate the dual superconductor hypothesis in finite-temperature SU(2) lattice gluodynamics in the spatial maximal Abelian gauge. This gauge is more physical than the ordinary maximal Abelian gauge due to absence of nonlocalities in the temporal direction. We show numerically that in the spatial maximal Abelian gauge the probability distribution of the Abelian monopole field is consistent with the dual superconductor mechanism of confinement: the Abelian condensate vanishes in the deconfinement phase and is nonzero in the confinement phase. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 3, 166–170 (10 February 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Phase structure of the SU(2) lattice gauge Higgs theory

Phase structure of the SU(2) lattice gauge Higgs theory is investigated by the Monte Carlo method and by an approximate calculation of an effective potential. Higgs fields are considered in the fundamental representation, and the radial mode of Higgs fields is not frozen. Two different radial measures for a radially varied Higgs field are used.Phase diagrams of the theory are determined, and a strong dependence on the choice of radial measure of scalar fields is manifested.     

Confining string formed by P vortices in the indirect Z(2) projection of SU(2) lattice gauge theory

We study the distribution of P vortices near the confining string in the indirect _Z(2) projection of SU(2) lattice gauge theory. We find that the density of vortices approaches the vacuum value at large distances and is strongly suppressed near the line connecting the test quark-antiquark pair. This implies that the condensate of P vortices is broken inside the confining string. The width of the _P-vortex density distribution increases with increasing distance between the quark and antiquark. Our best fit indicates the logarithmic dependence of this width on q q? separation.