论文标题
关于量子极端表面公式的批量解释的注释
A note on the bulk interpretation of the Quantum Extremal Surface formula
论文作者
论文摘要
由于时空的波动，直接定义量子信息数量直接在大量量子重力中定义是一个困难的问题。最近在\ cite {Mertens：2022ujr}中取得了一些进展，该进展提供了对Bekenstein Hawking公式的批量解释，该公式就重力边缘模式的纠缠熵而言，针对两个方面的BTZ黑洞。我们将这些结果概括为在ADS3重力中对量子极端表面公式进行大量的纠缠熵解释，如边界理论中的单个间隔。我们的计算进一步支持了一个建议，即ADS3重力可以被视为拓扑阶段，其中散装重力边缘模式是在量子组$ \ sl^{+} _ {q} _ {q}（2，\ mathbb {r}）$下转换下的。当我们切割沿块状共二维2切片打开欧几里得路径积分时，这些边缘模式出现，并满足可收缩的边界条件，以确保长臂猿的计算得出正确的状态计数。
Defining quantum information quantities directly in bulk quantum gravity is a difficult problem due to the fluctuations of spacetime. Some progress was made recently in \cite{Mertens:2022ujr}, which provided a bulk interpretation of the Bekenstein Hawking formula for two sided BTZ black holes in terms of the entanglement entropy of gravitational edge modes. We generalize those results to give a bulk entanglement entropy interpretation of the quantum extremal surface formula in AdS3 gravity, as applied to a single interval in the boundary theory. Our computation further supports the proposal that AdS3 gravity can be viewed as a topological phase in which the bulk gravity edge modes are anyons transforming under the quantum group $\SL^{+}_{q}(2,\mathbb{R})$. These edge modes appear when we cut open the Euclidean path integral along bulk co-dimension 2 slices, and satisfies a shrinkable boundary condition which ensures that the Gibbons-Hawking calculation gives the correct state counting.
