Fractal dimension of the topological charge density distribution in SU(2) lattice gluodynamics

Topological clusters in SU(2) gluodynamics at finite temperature and the evidence for KvB calorons

We report on our search for Kraan-van Baal calorons in finite temperature SU(2) lattice ensembles. We also discuss recent progress made in developing a caloron-anticaloron gas model decribing confinement and deconfinement in the context of trivial and non-trivial holonomy.

Study of the topological vacuum structure of SU(2) gluodynamics at T > 0 with overlap fermions and improved action

We study SU(2) gluodynamics at finite temperature near the deconfining phase transition. We create the lattice ensembles using the tadpole improved Luscher-Weisz action. The overlap Dirac operator is used to determine the following three aspects of vacuum structure: (i) The topological susceptibility is evaluated at various temperatures across the phase transition, (ii) the overlap fermion spectral density is determined and found to depend on the Polyakov loop above the phase transition and (iii) the corresponding localization properties of low lying eigenmodes are investigated.

The topological structure of SU(2) gluodynamics at T > 0 : an analysis using the Symanzik action and Neuberger overlap fermions

We study SU(2) gluodynamics at finite temperature on both sides of the deconfining phase transition. We create the lattice ensembles using the tree-level tadpole-improved Symanzik action. The Neuberger overlap Dirac operator is used to determine the following three aspects of vacuum structure: (i) The topological susceptibility is evaluated at various temperatures across the phase transition, (ii) the overlap fermion spectral density is determined and found to depend on the Polyakov loop above the phase transition and (iii) the corresponding localization properties of low-lying eigenmodes are …

Central Dominance and the Confinement Mechanism in Gluodynamics

New topological objects, which we call center monopoles, naturally arise in the Maximal Center Projection of SU(3) gluodynamics. The condensate of the center monopoles is the order parameter of the theory.

Topology near the transition temperature in lattice gluodynamics analyzed by low lying modes of the overlap Dirac operator

Topological objects of $SU(3)$ gluodynamics are studied at the infrared scale near the transition temperature with the help of zero and near-zero modes of the overlap Dirac operator. We construct UV filtered topological charge densities corresponding to three versions of the temporal boundary condition applied to this operator, for which the zero mode is known to be located on corresponding three constituent dyons (antidyons) in the reference case of an analytical (anti)caloron solution. The clustering of the three topological charge densities marks the positions of three types of dyons and an…

SU(2) Gluodynamics and HP1 sigma-model embedding: Scaling, Topology and Confinement

We investigate recently proposed HP1 sigma-model embedding method aimed to study the topology of SU(2) gauge fields. The HP1 based topological charge is shown to be fairly compatible with various known definitions. We study the corresponding topological susceptibility and estimate its value in the continuum limit. The geometrical clarity of HP1 approach allows to investigate non-perturbative aspects of SU(2) gauge theory on qualitatively new level. In particular, we obtain numerically precise estimation of gluon condensate and its leading quadratic correction. Furthermore, we present clear evi…

Blocking from continuum and monopoles in gluodynamics

We review the method of blocking of topological defects from continuum used as a non--perturbative tool to construct effective actions for these defects. The actions are formulated in the continuum limit while the couplings of these actions can be derived from simple observables calculated numerically on lattices with a finite lattice spacing. We demonstrate the success of the method in deriving the effective actions for Abelian monopoles in the pure SU(2) gauge models in an Abelian gauge. In particular, we discuss the gluodynamics in three and four space--time dimensions at zero and non--zero…

“$SU(2)$晶格Gluodynamics的各种阿贝尔投影中的禁闭机制”

"Confinement Mechanism in Various Abelian Projections of $SU(2)$ Lattice Gluodynamics"

我们证明了格点胶子动力学中的量子禁闭机制是最大阿贝尔投影的一个特殊特征。我们给出了一个明确的例子的$SU(2) \rightarrow U(1)$投影（最小阿贝尔投影），其中的限制是由于拓扑对象以外的单极。我们进行分析和数值研究的循环扩展的Faddeev-Popov行列式的最大和最小的阿贝尔投影，并讨论了这些投影的基本模块区域。

Dyon structures in the deconfinement phase of lattice gluodynamics: topological clusters, holonomies and Abelian monopoles

The topological structure of lattice gluodynamics is studied at intermediate resolution scale in the deconfining phase with the help of a cluster analysis. UV filtered topological charge densities are determined from a fixed number of low-lying eigenmodes of the overlap Dirac operator with three types of temporal boundary conditions applied to the valence quark fields. This method usually allows to find all three distinguished (anti)dyon constituents in the gauge field of Kraan-van Baal-Lee-Lu (anti)caloron solutions. The clustering of the three topological charge densities in Monte Carlo gene…

Geometrical clusterization of Polyakov loops in SU(2) lattice gluodynamics

The liquid droplet formula is applied to an analysis of the properties of geometrical (anti)clusters formed in SU(2) gluodynamics by the Polyakov loops of the same sign. Using this approach, we explain the phase transition in SU(2) gluodynamics as a transition between two liquids during which one of the liquid droplets (the largest cluster of a certain Polyakov loop sign) experiences a condensation, while the droplet of another liquid (the next to the largest cluster of the opposite sign of Polyakov loop) evaporates. The clusters of smaller sizes form two accompanying gases, which behave oppos…

格点胶子动力学各种阿贝尔投影中的禁闭机制

Confinement Mechanism in Various Abelian Projections of Lattice Gluodynamics

我们指出，格点胶子动力学中的量子禁闭机制可能是最大阿贝尔投影的一个特殊特征。我们给出了一个明确的例子的$SU(2) \rightarrow U(1)$投影（最小阿贝尔投影），其中的限制是由于拓扑对象以外的单极。我们还讨论了阿贝尔投影$SU(2)$胶子动力学的弦表示。

场论中$SU(2)$格点Gluodynamics的各种阿贝尔投影和Aharonov-Bohm效应

Various Abelian Projections of $SU(2)$ Lattice Gluodynamics and Aharonov-Bohm Effect in the Field Theory

我们表明，在一般的阿贝尔投影格点gluodynamics它不仅是单极子，但也弦。这两种拓扑激发可能是负责颜色的限制。我们说明了我们的想法在阿贝尔希格斯模型与恶棍行动的一些明确的结果。

规范固定缺陷的分形维数

Fractal Dimension of Gauge-fixing Defects

定义并计算了格点$SU(3)$胶子动力学中抵抗朗道或最大阿贝尔（MA）规范固定的格点的分维$D_f$.在朗道规范中，这些位置在限制相中聚成$D_f\sim 1$团簇。在有限的温度阶段，它们的维数下降到$D_f < 1$，也就是说，集群似乎消散。相比之下，MA规格耐网站未能表现出显着的趋势，集群在任何温度下。

Dyons near the transition temperature in $SU(3)$ lattice gluodynamics

We study the topological structure of $SU(3)$ lattice gluodynamics by cluster analysis. This methodological study is meant as preparation for full QCD. The topological charge density is becoming visible in the process of overimproved gradient flow, which is monitored by means of the the Inverse Participation Ratio (IPR). The flow is stopped at the moment when calorons dissociate into dyons due to the overimproved character of the underlying action. This gives the possibility to simultaneously detect all three dyonic constituents of KvBLL calorons in the gluonic field. The behaviour of the aver…

On topological properties of vacuum defects in lattice Yang-Mills theories

We study correlations between low-lying modes of the overlap Dirac operator and vacuum defects, center vortices and three-dimensional volumes, in lattice SU(2) gluodynamics. The low-lying modes are apparently sensitive to topological properties of the underlying gluon field configurations while the vacuum defects are crucial for the confinement. We find distinct positive correlation in both cases. In case of vortices the correlation is stronger.

More about the new non-selfdual axially symmetric SU(2) calorons

We describe the recently found non-selfdual axially symmetric caloron solutions of SU(2) gluodynamics with trivial holonomy. We present the local Polyakov loop together with the action and topological charge density. Different from the well-known KvBLL calorons, the calorons considered here are composed out of pseudoparticle constituents carrying integer topological charge. The loci of Polyakov loop L = -1 correspond to the loci of Higgs field zeroes for corresponding solutions of the Yang-Mills Higgs system. For certain parameters pointlike monopole pairs turn into rings.

Topological and magnetic properties of the QCD vacuum probed by overlap fermions

We study some of the local CP-odd and magnetic properties of the non-Abelian vacuum with use of overlap fermions within the quenched lattice gauge theory. Among these properties are the following: inhomogeneous spatial distribution of the topological charge density (chirality for massless fermions) in SU(2) gluodynamics (for uncooled gauge configurations the chirality is localized on low-dimensional defects with d=2..3, while a sequence of cooling steps gives rise to four-dimensional instantons and hence a four-dimensional structure of the chirality distribution); finite local fluctuations of …

使用分形拓扑码进行量子纠错

Quantum error correction with fractal topological codes

本文研究分形表面码作为容错量子存储器的纠错性能，改造 sweep decoder 处理比特翻转并用 MWPM 处理相位翻转，给出非零阈值及与禁闭-Higgs 相变的联系。