论文标题
差分熵和全息复杂性的第一定律
The first law of differential entropy and holographic complexity
论文作者
论文摘要
我们在三维广告时期构建了球形因果钻石第一定律的CFT双重。 ADS中的球形对称因果钻石$ _3 $是空间圆盘依赖性的领域，其外部曲率消失。批量第一法涉及磁盘边界区域的变化，磁盘的空间体积，宇宙常数和物质哈密顿量。在本文中，我们专门研究从纯AD到锥形缺陷时空的一阶度量变化，并且按照基于坐标的方法得出了批量第一定律。 ADS/CFT字典将磁盘边界的面积连接到CFT $ _2 $中的差分熵，并假设“复杂性=音量”猜想，则磁盘的体积被认为是对截止CFT的复杂性的双重偶性。在CFT侧，我们使用运动学空间形式主义明确计算真空状态的差分熵和全息复杂性，并计算出激发态双重圆锥形广告。结果，批量第一定律的边界双重双重双重双重二阶变化与激发态的缩放维度的缩放尺寸的变化有关，这与大体中的汉密尔顿变化相对应。我们还包括边界第一法中的中央电荷与相关化学势的变化。最后，我们评论了惠勒·戴维特（Wheeler-Dewitt）广告贴片的第一定律的边界双重双重双重双重双重双重双重双重偶，我们建议将CFT第一定律扩展到更高的维度。
We construct the CFT dual of the first law of spherical causal diamonds in three-dimensional AdS spacetime. A spherically symmetric causal diamond in AdS$_3$ is the domain of dependence of a spatial circular disk with vanishing extrinsic curvature. The bulk first law relates the variations of the area of the boundary of the disk, the spatial volume of the disk, the cosmological constant and the matter Hamiltonian. In this paper we specialize to first-order metric variations from pure AdS to the conical defect spacetime, and the bulk first law is derived following a coordinate based approach. The AdS/CFT dictionary connects the area of the boundary of the disk to the differential entropy in CFT$_2$, and assuming the `complexity=volume' conjecture, the volume of the disk is considered to be dual to the complexity of a cutoff CFT. On the CFT side we explicitly compute the differential entropy and holographic complexity for the vacuum state and the excited state dual to conical AdS using the kinematic space formalism. As a result, the boundary dual of the bulk first law relates the first-order variations of differential entropy and complexity to the variation of the scaling dimension of the excited state, which corresponds to the matter Hamiltonian variation in the bulk. We also include the variation of the central charge with associated chemical potential in the boundary first law. Finally, we comment on the boundary dual of the first law for the Wheeler-deWitt patch of AdS, and we propose an extension of our CFT first law to higher dimensions.
