We study holographic entanglement entropy in four-dimensional quantum gravity with negative cosmological constant. By using the replica trick and evaluating path integrals in the minisuperspace approximation, in conjunction with the Wheeler–DeWitt equation, we compute quantum corrections to the holographic entanglement entropy for a circular entangling surface on the boundary three-sphere. Similarly to our previous work on the sphere partition function, the path integrals are dominated by a replica version of asymptotically anti-de Sitter conic geometries at saddle points. As expected from a general conformal field theory argument, the final result is minus the free energy on the three-sphere, which agrees with the logarithm of the Airy partition function for the Aharony–Bergman–Jafferis–Maldacena theory that sums up all perturbative |$1/N$| corrections despite the absence of supersymmetries. The all-order holographic entanglement entropy cleanly splits into two parts, (1) the |$1/N$|-corrected Ryu–Takayanagi minimal surface area and (2) the bulk entanglement entropy across the minimal surface, as suggested in the earlier literature. It is explicitly shown that the former comes from the localized conical singularity of the replica geometries and the latter from the replication of the bulk volume.

中文翻译：

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1 / N扩展中所有阶的量子全息纠缠熵

我们研究具有负宇宙学常数的四维量子引力中的全息纠缠熵。通过使用复制技巧，并在微型超空间近似中评估路径积分，并结合Wheeler-DeWitt方程，我们对边界三球面上的圆形纠缠表面的全息纠缠熵进行了量子校正。与我们先前关于球面分割函数的工作类似，路径积分由在鞍点处渐近反de Sitter圆锥几何的副本版本控制。正如一般的共形场论论证所期望的那样，最终结果是减去三个球体上的自由能，这与Aharony-Bergman-Jafferis-Maldacena理论的Airy分区函数的对数一致，该理论总结了所有摄动| $ 1 / N $ | 尽管没有超对称性也可以进行校正。全阶全息纠缠熵清晰地分为两部分，（1）| $ 1 / N $ | 校正的Ryu–Takayanagi最小表面积和（2）跨越最小表面的体积纠缠熵，如早期文献中所建议。明确表明，前者来自复制体几何形状的局部圆锥形奇异性，而后者来自体积的复制。