论文标题
重力边缘模式的纠缠熵
Entanglement entropy of gravitational edge modes
论文作者
论文摘要
我们考虑了$ 4D $ Minkowski空间中的线性化重力，并将其分解为张量球形谐波并修复量规。高斯重力定律意味着在球体上的riemann张量的某些径向分量标记了重力的超选择性部门。我们表明，在Riemann张量的这6个正常组件中，有2个与球体中的量规不变运算符代数有关。从$ s^2 $上的这些分量的这些组件的两点函数中，我们计算了这些超选择扇区跨球面纠缠表面的纠缠熵的对数系数。对于由riemann张量的两个组件标记的扇区，这些系数相等，其总贡献由$ - \ frac {16} {3} $给出。我们观察到，该系数与从Harish-Chandra特征书写时从4-Sphere上无质量自旋2场的边缘分区函数中提取的系数一致。作为初步步骤，我们还评估了由$ U（1）$理论的径向组件标记的超选择性部门的纠缠熵的对数系数，甚至$ d $。我们表明，这与$ s^d $上的无质旋转1场的边缘Harish-Chandra角色的相应系数一致。
We consider the linearised graviton in $4d$ Minkowski space and decompose it into tensor spherical harmonics and fix the gauge. The Gauss law of gravity implies that certain radial components of the Riemann tensor of the graviton on the sphere label the superselection sectors for the graviton. We show that among these 6 normal components of the Riemann tensor, 2 are related locally to the algebra of gauge-invariant operators in the sphere. From the two-point function of these components of the Riemann tensor on $S^2$ we compute the logarithmic coefficient of the entanglement entropy of these superselection sectors across a spherical entangling surface. For sectors labelled by each of the two components of the Riemann tensor these coefficients are equal and their total contribution is given by $-\frac{16}{3}$. We observe that this coefficient coincides with that extracted from the edge partition function of the massless spin-2 field on the 4-sphere when written in terms of its Harish-Chandra character. As a preliminary step, we also evaluate the logarithmic coefficient of the entanglement entropy from the superselection sectors labelled by the radial component of the electric field of the $U(1)$ theory in even $d$ dimensions. We show that this agrees with the corresponding coefficient of the edge Harish-Chandra character of the massless spin-1 field on $S^d$.
