论文标题
在相关扰动下重新归一化的全息次区域复杂性
Renormalized Holographic Subregion Complexity under Relevant Perturbations
论文作者
论文摘要
我们在相关扰动下的CV猜想中构建了重新归一化的全息纠缠熵（HEE）和子区域复杂性（HSC），用于渐近广告$ _4 $ $ _4 $和ADS $ _5 $几何形状。使用仪表/重力二元性中开发的全息重新归一化方法，我们获得了在坐标选择下不变的反项。根据相关操作员在$ d = 3 $和$ d = 4 $ dual Field Theories中相关操作员的共形维度，我们明确定义了不同形式的重新归一化HEE和HSC。我们使用一般的嵌入来进行任意纠缠子区域，并表明坐标系的任何选择都给出了相同形式的计数器术语，因为它们是根据边界上的曲率不变性和标量字段编写的。我们展示了我们的一般过程的明确示例。有趣的是，我们发现，在相关的扰动中，HSC在渐近上的几何形状在与范围$ 0 <Δ<\ frac {1} {1} {1} {2} {2} {2} \，\，\，\，{\ rm and} $ be，通过添加任何坐标不变的计数器术语来取消。这意味着共形尺寸的这些范围内的HSC不是可重新分析的。
We construct renormalized holographic entanglement entropy (HEE) and subregion complexity (HSC) in the CV conjecture for asymptotically AdS$_4$ and AdS$_5$ geometries under relevant perturbations. Using the holographic renormalization method developed in the gauge/gravity duality, we obtain counter terms which are invariant under coordinate choices. We explicitly define different forms of renormalized HEE and HSC, according to conformal dimensions of relevant operators in the $d=3$ and $d=4$ dual field theories. We use a general embedding for arbitrary entangling subregions and showed that any choice of the coordinate system gives the same form of the counter terms, since they are written in terms of curvature invariants and scalar fields on the boundaries. We show an explicit example of our general procedure. Intriguingly, we find that a divergent term of the HSC in the asymptotically AdS$_5$ geometry under relevant perturbations with operators of conformal dimensions in the range $0< Δ< \frac{1}{2}\,\, {\rm and} \,\, \frac{7}{2}< Δ< 4$ cannot be cancelled out by adding any coordinate invariant counter term. This implies that the HSCs in these ranges of the conformal dimensions are not renormalizable covariantly.
