Decomposition in diverse dimensions
Decomposition in diverse dimensions
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多维度分解
DOI：
10.1103/physrevd.90.025030
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发表时间：
2014
影响因子：
5
通讯作者：
E. Sharpe
中科院分区：
文献类型：
--
作者：
E. Sharpe
本文讨论了二维和四维中由有限平凡作用中心规范群定义的规范理论与限制非微扰扇区的规范理论之间的关系。在两个维度上，这些概念似乎是一致的。推广了轨道折叠和阿贝尔规范理论的旧结果，我们提出了一种将具有中心不变物质的二维非阿贝尔规范理论分解为具有旋转离散θ角的理论的不相交和的方法;例如，示意性地，SU（2）= SO（3）_+ + SO（3）_-。我们验证了分解直接在纯非超对称二维杨米尔斯以及超对称理论。相比之下，在四维空间中，这些概念并不一致。为了澄清这种关系，我们讨论了通过限制非微扰扇区得到的理论。这些理论违反了集团分解，但我们说明了它们至少在特殊情况下可以被理解为行为良好的量子场论的不相交和，以及如何使用双子谱来区分例如对瞬子有限制的SO（3）理论和SU（2）理论。我们还简要地讨论了如何耦合各种类似的Dijkgraaf-Witten理论，通过耦合TQFT的QFT的瞬子限制的描述的一部分，可能会修改这些结果。
This paper discusses the relationships between gauge theories defined by gauge groups with finite trivially-acting centers, and theories with restrictions on nonperturbative sectors, in two and four dimensions. In two dimensions, these notions seem to coincide. Generalizing old results on orbifolds and abelian gauge theories, we propose a decomposition of two-dimensional nonabelian gauge theories with center-invariant matter into disjoint sums of theories with rotating discrete theta angles; for example, schematically, SU(2) = SO(3)_+ + SO(3)_-. We verify that decomposition directly in pure nonsupersymmetric two-dimensional Yang-Mills as well as in supersymmetric theories. In four dimensions, by contrast, these notions do not coincide. To clarify the relationship, we discuss theories obtained by restricting nonperturbative sectors. These theories violate cluster decomposition, but we illustrate how they may at least in special cases be understood as disjoint sums of well-behaved quantum field theories, and how dyon spectra can be used to distinguish, for example, an SO(3) theory with a restriction on instantons from an SU(2) theory. We also briefly discuss how coupling various analogues of Dijkgraaf-Witten theory, as part of a description of instanton restriction via coupling TQFT's to QFT's, may modify these results.