Rényi扭位移算符的引力对偶
Gravitational dual of the Rényi twist displacement operator
摘要：
我们给出了一个配方计算关联函数的位移算子定位在一个球形或平面的高维扭曲缺陷使用AdS/CFT。这样的扭曲算子通常用于构造CFTs中空间纠缠的$n$次Renyi熵，并且与具有双曲视界的黑洞全息对偶。位移算子则告诉我们，在纠缠表面的小形状变形下，Renyi熵是如何变化的。我们显式地构造了体积到边界的传播算子的位移算子插入作为一个线性化的度量波动的双曲黑洞，并使用它来提取系数的位移算子两点函数$C_D$在任何维度。扭转位移算符的$n \rightarrow 1$极限给出了与真空中插入零能算符相同的体响应，这与最近关于纠缠熵和模能量的形状依赖性的结果一致。
英文摘要：
We give a recipe for computing correlation functions of the displacement operator localized on a spherical or planar higher dimensional twist defect using AdS/CFT. Such twist operators are typically used to construct the $n$'th Renyi entropies of spatial entanglement in CFTs and are holographically dual to black holes with hyperbolic horizons. The displacement operator then tells us how the Renyi entropies change under small shape deformations of the entangling surface. We explicitly construct the bulk to boundary propagator for the displacement operator insertion as a linearized metric fluctuation of the hyperbolic black hole and use this to extract the coefficient of the displacement operator two point function $C_D$ in any dimension. The $n \rightarrow 1$ limit of the twist displacement operator gives the same bulk response as the insertion of a null energy operator in vacuum, which is consistent with recent results on the shape dependence of entanglement entropy and modular energy.
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