论文标题
副本相关器和模块化ETH的分析性
Analyticity of replica correlators and Modular ETH
论文作者
论文摘要
我们研究了本地运算符在$ n $表的复制歧管上的两个点相关函数，该复制歧管对应于保形场理论的真空状态中的半空间。与反向拉普拉斯变换类似，我们定义了此相关函数的renyi变换，该函数是一个复杂变量$ w $的函数，对Renyi参数$ n $ dual。受Caron-Huot的反转公式的启发，我们认为，如果Renyi Transform $ f（w）$在复杂的$ W $平面中具有无限的行为，那么Renyi Transform Discon Disce $ f（w）$的不连续性提供了原始Replica相关功能的$ N $ N $。我们通过明确计算大型$ n $全息cft $ _d $ in Dimensions $ d> 2 $中的特定副本相关器的Renyi变换来检查我们的公式。 我们还发现，Renyi变换的不连续性与模块化汉密尔顿的两个不同特征态之间的本地操作员的基质元素有关。我们计算了$ 2D $共形的场理论的Renyi变换，并使用它来提取（模块化）ETH的非对角元素。我们认为，在$ 2D $中，这等同于CFT的非对角线OPE系数，并表明我们的技术恰好再现了文献中最新的结果。
We study the two point correlation function of a local operator on an $n$-sheeted replica manifold corresponding to the half-space in the vacuum state of a conformal field theory. In analogy with the inverse Laplace transform, we define the Renyi transform of this correlation function, which is a function of one complex variable $w$, dual to the Renyi parameter $n$. Inspired by the inversion formula of Caron-Huot, we argue that if the Renyi transform $f(w)$ has bounded behavior at infinity in the complex $w$ plane, the discontinuity of the Renyi transform disc $f(w)$ provides the unique analytic continuation in $n$ of the original replica correlation function. We check our formula by explicitly calculating the Renyi transform of a particular replica correlator in a large $N$ holographic CFT$_d$ in dimensions $d>2$. We also discover that the discontinuity of the Renyi transform is related to the matrix element of local operators between two distinct eigenstates of the modular Hamiltonian. We calculate the Renyi transform in $2d$ conformal field theories, and use it to extract the off-diagonal elements of (modular) ETH. We argue that in $2d$, this is equivalent to the off-diagonal OPE coefficients of a CFT and show that our technique exactly reproduces recent results in the literature.
