arXiv 1211.06642012-11-04hep-lat

规范不变磁单极的弦张力

String tension from gauge invariant Magnetic Monopoles

Nigel Cundy, Weonjong Lee, Jaehoon Leem, Y. M. Cho

备注：: Lattice 2012 (Chiral Symmetry), 7 pages
发表信息：: PoS(Lattice 2012)213

摘要：

我们研究了色禁闭和由Cho-Duan-Ge分解得到的单极子之间的关系。这些磁单极不像狄拉克和特胡夫特磁单极，不需要一个奇异的规范场，并且可以定义为任意的规范场（而不仅仅限于最大阿贝尔规范）。阿贝尔分解定义的颜色字段$n$，我们的研究的原则新颖性是，我们使用了一个独特的定义，这个领域的特征向量的威尔逊圈。这使我们能够调查规范不变的单极子和禁闭之间的关系，分析和数值，以及保留最大可能的对称性内的颜色字段，使其能够看到所有的单极子在SU（$N_C$）计算。我们描述了阿贝尔分解是如何与威尔逊圈相关的，因此弦的张力可以从与分解的（或限制的）阿贝尔场相关的场强计算出来。我们讨论了色场中可能引起威尔逊圈中面积律的结构，这些结构是磁单极子。如果这些单极子存在，它们将导致威尔逊圈的面积定律缩放，因此至少部分地负责约束。我们在猝灭的格点量子色动力学中寻找这些单极子。我们表明，弦的张力是占主导地位的峰值的限制场强度，其中至少有一些位于接近结构的色场与理论预期的单极子。我们表明，弦张力提取的限制领域的贡献是接近整个原始领域的，再次表明，限制至少可以部分地解释在这些单极。

英文摘要：

We investigate the relationship between colour confinement and the monopoles derived from the Cho-Duan-Ge decomposition. These monopoles, unlike Dirac and 't Hooft monopoles, do not require a singular gauge field and are defined for any choice of gauge (and are not just restricted to, for example, the maximum Abelian gauge). The Abelian decomposition is defined in terms of a colour field $n$; the principle novelty of our study is that we have used a unique definition of this field in terms of the eigenvectors of the Wilson Loop. This allows us to investigate the relationship between the gauge invariant monopoles and confinement both analytically and numerically, as well as retaining the maximal possible symmetry within the colour field so that it is able to see all the monopoles in an SU($N_C$) calculation. We describe how the Abelian decomposition is related to the Wilson Loop, so that the string tension may be calculated from the field strength related to the decomposed (or restricted) Abelian field. We discuss the structures in the colour field which may cause an area law in the Wilson Loop, which turn out to be magnetic monopoles. If these monopoles are present, they will lead to an area law scaling of the Wilson Loop and thus be at least partially responsible for confinement. We search for these monopoles in quenched lattice QCD. We show that the string tension is dominated by peaks in the restricted field strength, at least some of which are located close to structures in the colour field consistent with with theoretical expectations for the monopoles. We show that the string tension extracted from the monopole contribution to the restricted field is close to that of the entire original field; again suggesting that confinement can at least partially be explained in terms of these monopoles.

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英文摘要：

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