论文标题
在运动空间中的浆果曲率和黎曼曲率和球形纠缠的表面
Berry Curvature and Riemann Curvature in Kinematic Space with Spherical Entangling Surface
论文作者
论文摘要
我们发现，在锚定在球形纠缠表面上的最小表面的任何运动学空间中，浆果曲率与黎曼曲率张量之间的联系。这一新的全息原理从模块化的哈密顿量的自动范围内建立了在任意维度的运动空间中的riemann几何形状，在更高的维度中，它由CFT $ _1 $ _1 $和CFT $ _2 $中的两对时类的分离点指定。我们构建的浆果曲率也具有所有几何形状的Riemann曲率的相同特性：内部对称性；偏斜对称；第一个Bianchi身份。我们得出模块化哈密顿量的代数及其变形，后者可以为模块化的模式提供最大的模块化混乱。代数还决定平行运输，这导致浆果曲率与Riemann曲率张量完全匹配。最后，我们将CFT $ _1 $与更高维的CFT进行了比较，并显示了与OPE块的差异。
We discover the connection between the Berry curvature and the Riemann curvature tensor in any kinematic space of minimal surfaces anchored on spherical entangling surfaces. This new holographic principle establishes the Riemann geometry in kinematic space of arbitrary dimensions from the holonomy of modular Hamiltonian, which in the higher dimensions is specified by a pair of time-like separated points as in CFT$_1$ and CFT$_2$. The Berry curvature that we constructed also shares the same property of the Riemann curvature for all geometry: internal symmetry; skew symmetry; first Bianchi identity. We derive the algebra of the modular Hamiltonian and its deformation, the latter of which can provide the maximal modular chaos to the modular scrambling modes. The algebra also dictates the parallel transport, which leads to the Berry curvature exactly matching to the Riemann curvature tensor. Finally, we compare CFT$_1$ to higher dimensional CFTs and show the difference from the OPE block.
