θ依赖、符号问题与拓扑干涉
Theta dependence, sign problems and topological interference
摘要：
在规范理论和量子力学的欧几里德路径积分公式中，θ项导致了一个符号问题，并相应地导致了拓扑缺陷逸度的复相位;而在闵可夫斯基公式中，它导致了一个拓扑（几何）相位乘以普通路径振幅。在一个SU（2）Yang-Mills理论中，我们证明了复逸度在欧氏路径历史之间产生干涉，即，从根本上改变了真空结构。在θ =0时，质量间隙是由于库仑瞬子等离子体，并且该理论具有唯一的真空。在θ = π时，由于相消的拓扑干涉，尽管θ密度与θ无关，但θ诱导的质量间隙消失了。这个理论有两种选择：保持无间隙或被一个双重简并真空所间隙。我们证明后者是通过磁生物机制实现的，而双真空是CP自发破缺的实现。圆紧化规范理论中的θ项效应是Aharonov-Bohm效应和几何（Berry）相位的推广。当θ从0变化到π时，规范理论在两个空间维二分晶格上的偶数和奇数自旋量子反铁磁体之间插值，这两个晶格分别具有基态简并1和2，就像在规范理论中θ =0和θ = π时一样。
英文摘要：
In a Euclidean path integral formulation of gauge theory and quantum mechanics, the theta-term induces a sign problem, and relatedly, a complex phase for the fugacity of topological defects; whereas in Minkowskian formulation, it induces a topological (geometric) phase multiplying ordinary path-amplitudes. In an SU(2) Yang-Mills theory which admits a semi-classical limit, we show that the complex fugacity generates interference between Euclidean path histories, i.e., monopole-instanton events, and radically alters the vacuum structure. At theta=0, a mass gap is due to the monopole-instanton plasma, and the theory has a unique vacuum. At theta=pi, the monopole induced mass gap vanishes, despite the fact that monopole density is independent of theta, due to destructive topological interference. The theory has two options: to remain gapless or to be gapped with a two-fold degenerate vacua. We show the latter is realized by the magnetic bion mechanism, and the two-vacua are realization of spontaneous CP-breaking. The effect of the theta-term in the circle-compactified gauge theory is a generalization of Aharonov-Bohm effect, and the geometric (Berry) phase. As theta varies from 0 to pi, the gauge theory interpolates between even- and odd-integer spin quantum anti-ferromagnets on two spatial dimensional bi-partite lattices, which have ground state degeneracies one and two, respectively, as it is in gauge theory at theta=0 and theta=pi.
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