arXiv 2201.060432022-01hep-thgr-qc

引力边缘模的纠缠熵

Entanglement entropy of gravitational edge modes

Justin R. David, Jyotirmoy Mukherjee

备注：: Typos corrected
DOI：: 10.1007/JHEP08(2022)065

摘要：

考虑$4d$ Minkowski空间中的线性引力子，将其分解为张量球谐函数，并固定了规范。高斯引力定律意味着引力子的黎曼张量在球上的某些径向分量标记了引力子的超选择扇区。我们表明，在这6个正规分量的黎曼张量，2是局部相关的规范不变的运营商在球的代数。从$S^2$上的黎曼张量的这些分量的两点函数，我们计算了这些超选择扇区在球形纠缠表面上的纠缠熵的对数系数。对于由黎曼张量的两个分量中的每一个标记的扇区，这些系数是相等的，并且它们的总贡献由$-\frac{16}{3}$给出。我们观察到，这个系数与提取的边缘配分函数的无质量自旋2场的4-球时，书面的哈里什-钱德拉字符。作为一个初步的步骤，我们还评估了对数系数的纠缠熵标记的径向分量的电场的$U(1)$理论，甚至$d$尺寸的超选择部门。我们证明了这与$S^d$上无质量自旋为1的场的边缘Harish-Chandra特征的相应系数一致。

英文摘要：

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 $S^d$.

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