arXiv 1504.058102015-04-22hep-th

$QCD$中的陈-西蒙斯-施温格约束模型

Chern-Simons-Schwinger model of confinement in $QCD$

Antonio Aurilia, Patricio Gaete, Euro Spallucci

备注：: 15 pages

摘要：

结果表明，在杨-米尔斯理论的强耦合极限下，胶袋的形成机制可以用高阶阿贝尔规范场的动力学来理解，即Chern-Simons拓扑流的3-形式对偶.在此基础上，我们表明，陈-西蒙斯项的场论解释，而不是其拓扑解释，也导致了分析形式的限制潜力，出现在大距离限制的$QCD$。事实上，对于Schwinger模型的$(3+1)$维推广，我们明确地计算相互作用能。这种推广是由于拓扑规范场$A_{μνρ}$的存在。我们的结果表明，静态电位分布包含一个线性项，导致静态探针电荷的限制。一旦考虑到$QCD$中轴向矢量异常的量子效应，新的规范场及其物质流对应物就提供了$QED_2$中“电荷屏蔽”的施温格机制的精确复制品。

英文摘要：

It has been shown that the mechanism of formation of glue-bags in the strong coupling limit of Yang-Mills theory can be understood in terms of the dynamics of a higher-rank abelian gauge field, namely, the 3-form dual to the Chern-Simons topological current. Building on this result, we show that the field theoretical interpretation of the Chern-Simons term, as opposed to its topological interpretation, also leads to the analytic form of the confinement potential that arises in the large distance limit of $QCD$. In fact, for a $(3+1)$-dimensional generalization of the Schwinger model, we explicitly compute the interaction energy. This generalization is due to the presence of the topological gauge field $A_{μνρ}$. Our results show that the static potential profile contains a linear term leading to the confinement of static probe charges. Once the quantum effects of the axial vector anomaly in $QCD$ are taken into account, the new gauge field and its matter-current counterpart provide an exact replica of the Schwinger mechanism of "charge-screening" that operates in $QED_2$.

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