论文标题
CFT $ _2 $基态的截止依赖性和复杂性
Cutoff Dependence and Complexity of the CFT$_2$ Ground State
论文作者
论文摘要
我们介绍了二维形式的保形场理论（CFT $ _2 $）作为Wilson线网络中的$ SL（2，\ Mathbb {r}）\ Times SL（2，\ Mathbb {r}）$ Chern-Simons的网络，该理论通常用于研究三维抗议Serti anti-De-De-De-De-De-De-De-de-de-de-de-de-de-de-de-de-de-de-de-de-de-de-de-de-de-de-de-de-de sitter $。网络的位置和形状编码定义基态密度运算符的截止比例。一个普遍的论点表明，通过ADS $ _3 $中的截止表面的外部曲率识别该网络的“复杂性”，而Gauss-bonnet定理与全息图相一致。
We present the vacuum of a two-dimensional conformal field theory (CFT$_2$) as a network of Wilson lines in $SL(2,\mathbb{R}) \times SL(2,\mathbb{R})$ Chern-Simons theory, which is conventionally used to study gravity in three-dimensional anti-de Sitter space (AdS$_3$). The position and shape of the network encode the cutoff scale at which the ground state density operator is defined. A general argument suggests identifying the `density of complexity' of this network with the extrinsic curvature of the cutoff surface in AdS$_3$, which by the Gauss-Bonnet theorem agrees with the holographic Complexity = Volume proposal.
