论文标题
3D量子重力及其大量分解的建议
A proposal for 3d quantum gravity and its bulk factorization
论文作者
论文摘要
AD/CFT的最新进展提供了对边界CFT的纠缠结构中散装时空的编码的充分理解。然而，关于时空是如何直接来自批量量子理论，知之甚少。我们在有效的3D量子理论中解决了这个问题，该理论描述了全息CFT的高温状态。该理论可以看作是$ q $的形式和JT重力的尺寸提升。使用此模型，我们表明，双面黑洞的Bekenstein-Hawking熵等于重力边缘模式的庞大纠缠熵。在传统的Chern-Simons描述中，这些黑洞对应于$ \ psl（2，\ Mathbb {r}）\ otimes \ psl（2，\ Mathbb {r}）$的Wilson Lines。 We show that the correct calculation of gravitational entropy suggests we should interpret the bulk theory as an extended topological quantum field theory associated to the quantum semi-group $\SL^+_{q}(2,\mathbb{R})\otimes \SL^+_{q}(2,\mathbb{R})$.我们的计算表明，在集体，任何自由度的自由度方面，有效描述了散装微骨，其纠缠导致散装时空的出现。
Recent progress in AdS/CFT has provided a good understanding of how the bulk spacetime is encoded in the entanglement structure of the boundary CFT. However, little is known about how spacetime emerges directly from the bulk quantum theory. We address this question in an effective 3d quantum theory of pure gravity, which describes the high temperature regime of a holographic CFT. This theory can be viewed as a $q$-deformation and dimensional uplift of JT gravity. Using this model, we show that the Bekenstein-Hawking entropy of a two-sided black hole equals the bulk entanglement entropy of gravitational edge modes. In the conventional Chern-Simons description, these black holes correspond to Wilson lines in representations of $\PSL(2,\mathbb{R})\otimes \PSL(2,\mathbb{R}) $. We show that the correct calculation of gravitational entropy suggests we should interpret the bulk theory as an extended topological quantum field theory associated to the quantum semi-group $\SL^+_{q}(2,\mathbb{R})\otimes \SL^+_{q}(2,\mathbb{R})$. Our calculation suggests an effective description of bulk microstates in terms of collective, anyonic degrees of freedom whose entanglement leads to the emergence of the bulk spacetime.
