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Intersections of thick Center Vortices, Dirac Eigenmodes and Fractional Topological Charge in SU(2) Lattice Gauge Theory

机译:厚中心涡,狄拉克本征模和分数阶的交点   sU(2)格点规范理论中的拓扑电荷

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摘要

Intersections of thick, plane SU(2) center vortices are characterized by thetopological charge |Q|=1/2. We compare such intersections with the distributionof zeromodes of the Dirac operator in the fundamental and adjointrepresentation using both the overlap and asqtad staggered fermion formulationsin SU(2) lattice gauge theory. We analyze configurations with fourintersections and find that the probability density distribution of fundamentalzeromodes in the intersection plane differs significantly from the one obtainedanalytically in [Phys.\ Rev.\ D 66, 85004 (2002)]. The Dirac eigenmodes areclearly sensitive to the traces of the Polyakov (Wilson) lines and do notexactly locate topological charge contributions. Although, the adjoint Diracoperator is able to produce zeromodes for configurations with topologicalcharge |Q|=1/2, they do not locate single vortex intersections, as we prove byforming arbitrary linear combinations of these zeromodes - their scalar densitypeaks at least at two intersection points. With pairs of thin and thickvortices we realize a situation similar to configurations with topologicalcharge |Q|=1/2. For such configurations the zeromodes do not localize in theregions of fractional topological charge contribution but spread over the wholelattice, avoiding regions of negative traces of Polyakov lines.
机译:厚的平面SU(2)中心漩涡的交点的特征是拓扑电荷| Q | = 1/2。我们使用SU(2)晶格规理论中的重叠和asqtad交错费米子公式,将这种相交与Dirac算子在基本表示和伴随表示中零模式的分布进行比较。我们分析了具有四个相交的配置,发现相交平面中基本零模的概率密度分布与[Phys.Rev.D 66,85004(2002)]解析得到的相差很大。 Dirac本征模式对Polyakov(Wilson)谱线的迹线显然很敏感,并且没有精确定位拓扑电荷的贡献。尽管伴随Diracoperator能够为拓扑电荷| Q | = 1/2的配置生成零模,但它们无法定位单个涡旋相交,正如我们通过形成这些零模的任意线性组合所证明的那样-它们的标量密度至少在两个交点处达到峰值。利用成对的薄涡旋和厚涡旋,我们实现了类似于拓扑电荷| Q | = 1/2的配置的情况。对于这样的配置,零模不在局部拓扑电荷贡献的区域中,而是散布在整个晶格上,从而避免了Polyakov线的负迹线区域。

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