Tsujimura Jun, Nambu Yasusada
Department of Physics, Graduate School of Science, Nagoya University, Chikusa, Nagoya 464-8602, Japan.
Entropy (Basel). 2020 Nov 14;22(11):1297. doi: 10.3390/e22111297.
The Ryu-Takayanagi formula provides the entanglement entropy of quantum field theory as an area of the minimal surface (Ryu-Takayanagi surface) in a corresponding gravity theory. There are some attempts to understand the formula as a flow rather than as a surface. In this paper, we consider null rays emitted from the AdS boundary and construct a flow representing the causal holographic information. We present a sufficient and necessary condition that the causal information surface coincides with Ryu-Takayanagi surface. In particular, we show that, in spherical symmetric static spacetimes with a negative cosmological constant, wave fronts of null geodesics from a point on the AdS boundary become extremal surfaces and therefore they can be regarded as the Ryu-Takayanagi surfaces. In addition, from the viewpoint of flow, we propose a wave optical formula to calculate the causal holographic information.
龙谷-高柳公式将量子场论的纠缠熵表示为相应引力理论中最小曲面（龙谷-高柳曲面）的面积。有一些尝试将该公式理解为一种流而非一个曲面。在本文中，我们考虑从反德西特（AdS）边界发射的类光射线，并构建一个表示因果全息信息的流。我们给出了因果信息曲面与龙谷-高柳曲面相一致的充分必要条件。特别地，我们表明，在具有负宇宙学常数的球对称静态时空中，来自AdS边界上一点的类光测地线的波前成为极值曲面，因此它们可被视为龙谷-高柳曲面。此外，从流的观点出发，我们提出一个波动光学公式来计算因果全息信息。
