论文标题
反射熵的页面曲线
The Page Curve for Reflected Entropy
论文作者
论文摘要
我们在西海岸模型中研究了反射的熵$ S_R $，这是一个黑洞蒸发的玩具模型，由JT重力组成，耦合到世界末日的麸皮。我们证明了全息二元性与纠缠楔形截面有关的有效性，远离相变。此外，我们分析了重要的非扰动效应，这些效应使$ S_R $相变的不连续性平滑。通过执行重力路径积分，我们通过分析获得反射的纠缠谱。频谱采用了一个由超选择扇区组成的简单形式，我们将其解释为直接的几何形状总和，是断开连接的几何和涉及封闭宇宙的连接的总和。我们发现，$ O（\ sqrt {g_n}）$的面积波动分布在规范集合中的$ s_r $相变，类似于纠缠熵相变。我们还考虑了反射熵的Renyi概括，并表明相变的位置随Renyi参数的函数而变化。
We study the reflected entropy $S_R$ in the West Coast Model, a toy model of black hole evaporation consisting of JT gravity coupled to end-of-the-world branes. We demonstrate the validity of the holographic duality relating it to the entanglement wedge cross section away from phase transitions. Further, we analyze the important non-perturbative effects that smooth out the discontinuity in the $S_R$ phase transition. By performing the gravitational path integral, we obtain the reflected entanglement spectrum analytically. The spectrum takes a simple form consisting of superselection sectors, which we interpret as a direct sum of geometries, a disconnected one and a connected one involving a closed universe. We find that area fluctuations of $O(\sqrt{G_N})$ spread out the $S_R$ phase transition in the canonical ensemble, analogous to the entanglement entropy phase transition. We also consider a Renyi generalization of the reflected entropy and show that the location of the phase transition varies as a function of the Renyi parameter.
