共形场论中纠缠熵与模核性
Entanglement Entropy in CFT and Modular Nuclearity
AI总结：
本文研究了共形场论中纠缠熵的有限性，证明了真空态的规范纠缠熵在广泛共形网类中有限，并探讨了模$p$-核性条件对局部量子场论中互信息有限性的影响。
摘要：
在算子代数量子场论框架下，可以将几种算子代数意义上的纠缠熵与任何因果不相交的时空区域$\mathcal{S}_A$和$\mathcal{S}_B$配对，且具有正相对距离。其中，规范纠缠熵被定义为一个规范中间型I因子的冯·诺依曼熵。在本工作中，我们证明真空态的规范纠缠熵对于包括$U(1)$电流模型和$SU(n)$环群模型在内的广泛共形网类是有限的。由于先前研究指出这一有限性性质与系统的核性性质相关，我们展示了在满足某种$0 < p < 1$的模$p$-核性条件的任何局部量子场论中，互信息也是有限的。本文还为另一种引入的纠缠熵概念建立了类似的有限性结果。最后，我们对这一方向的未来工作进行了评论。
英文摘要：
In the framework of Algebraic Quantum Field Theory, several operator algebraic notions of entanglement entropy can be associated with any pair of causally disjoint spacetime regions $\mathcal{S}_A$ and $\mathcal{S}_B$ with positive relative distance. Among them, the canonical entanglement entropy is defined as the von Neumann entropy of a canonical intermediate type I factor. In this work, we show that the canonical entanglement entropy of the vacuum state is finite for a broad class of conformal nets including the $U(1)$-current model and the $SU(n)$-loop group models. Since previous studies suggest that this finiteness property is related to nuclearity properties of the system, we show that the mutual information is finite in any local QFT satisfying a modular $p$-nuclearity condition for some $0 < p < 1$. A similar finiteness result is established for another notion of entanglement entropy introduced in this paper. We conclude with remarks for future work in this direction.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
