论文标题
因果阴影和非本地模块化流：从堕落到扰动创世纪
Causal shadow and non-local modular flow: from degeneracy to perturbative genesis by correlation
论文作者
论文摘要
因果阴影是纠缠楔与因果楔之间的庞大时空区域，它们的存在在ADS/CFT中的次区域双重性的背景下编码纠缠楔重建的深度方面。在本文中，我们研究了因果阴影的扰动理论及其与相关模块化流量的特性的关系。我们首先根据已知示例重新审视退化因果阴影的案例，并通过模块化流的局部性质讨论其退化的起源。然后，我们专注于CFT子区域由两个球体组成的扰动案例，由大距离$ l \ gg r_ {1,2} $组成。 RT表面仍然与因果范围一致，从而经典地给出了堕落的因果阴影。我们从批量的互信息中计算到量子极端表面（q.e.s）的校正，然后以$ g_n $的顺序产生非分类因果阴影。最后，我们更普遍地讨论了因果阴影扰动理论，特别是我们探索了提取边界CFT中表征扰动因果阴影的阳性条件的可能性。
Causal shadows are bulk space-time regions between the entanglement wedges and the causal wedges, their existence encodes deep aspects of the entanglement wedge reconstruction in the context of subregion duality in AdS/CFT. In this paper, we study the perturbation theory of the causal shadows and their relation to the properties of the associated modular flows. We first revisit the cases of degenerate causal shadows based on known examples, and discuss the origin for their degeneracy via the local nature of the modular flow. We then focus on the perturbative case in which the CFT subregion consists of two spheres separated by a large distance $L\gg R_{1,2}$. The RT surfaces still agree with the causal horizons, giving a degenerate causal shadow classically. We compute the corrections to the quantum extremal surfaces (Q.E.S) from the bulk mutual information, which then give rise to a non-degenerate causal shadow at order $G_N$. We end by discussing the causal shadow perturbation theory more generally, in particular we explore the possibility of extracting the positivity conditions characterizing perturbative causal shadows in the boundary CFTs.
