模糊空间上相互作用标量理论的纠缠熵
Entanglement Entropy of Interacting Scalar Theories on Fuzzy Spaces
- Dept of Physics, College of Exact Sciences, Hamma Lakhdar University, El Oued, Algeria（哈马·拉赫达尔大学精确科学学院物理系）
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AI总结：
本文研究模糊空间上相互作用标量场的纠缠熵，发现相互作用修正具有广泛的体贡献，并探讨其与非交换场论中紫外/红外混合现象的联系。
AI中文摘要：
我们研究了自相互作用对$(2+1)$维时空中标量场的Rényi熵和纠缠熵的影响，其中空间截面由模糊空间建模，具体为模糊球面和模糊圆盘。我们使用格林函数方法计算了由$\lambda\phi^4$相互作用引起的一阶微扰修正。与自由理论（其中纠缠熵由纠缠边界附近的自由度主导并遵循面积律）相反，我们发现相互作用修正具有广泛的体贡献，从整个模糊空间中的自由度接收到显著贡献。对于模糊球面，该修正表现出与零模相关的强红外敏感性。我们通过投影掉零模来隔离并解决这一零模红外发散，从而获得物理上有意义的量。在交换连续极限中，相互作用修正具有与自由熵相同程度的紫外发散，但不遵循纯面积律。此外，我们分析了Moyal平面极限，其中相互作用修正表现出不同的红外发散。我们讨论了这些广泛体特征的物理起源，并考察了它们与非交换量子场论中著名的紫外/红外混合现象的可能联系。
英文摘要：
We investigate the impact of self-interactions on the Rényi and entanglement entropies of a scalar field on $(2+1)$-dimensional spacetimes, whose spatial sections are modeled by fuzzy spaces, specifically the fuzzy sphere and the fuzzy disc. We compute the first-order perturbative correction induced by a $λϕ^4$ interaction using the Green's function approach. In contrast to the free theory, where the entanglement entropy is dominated by degrees of freedom near the entangling boundary and obeys an area law, we find that the interaction correction has an extensive bulk contribution, receiving significant contributions from degrees of freedom throughout the fuzzy space. For the fuzzy sphere, the correction exhibits strong infrared sensitivity associated with the zero mode. We isolate and resolve this zero-mode IR divergence by projecting out the zero mode, thereby obtaining a physically meaningful quantity. In the commutative continuum limit, the interaction correction has the same degree of UV divergence as the free entropy but does not obey a pure area law. Furthermore, we analyze the Moyal plane limit, where the interaction correction exhibits a distinct IR divergence. We discuss the physical origin of these extensive bulk features and examine their possible connection to the celebrated UV/IR mixing phenomenon in noncommutative quantum field theories.
