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arXiv 2007.07444hep-thgr-qc
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来自虫洞的自由能量

Free Energy from Replica Wormholes

Netta Engelhardt, Sebastian Fischetti, Alexander Maloney

摘要:

欧几里德虫洞--连接不连通边界的几何形状--对该理论的标准量子力学解释提出了挑战。一个可能的解决办法是引力路径积分计算许多理论的系综平均。连接的拓扑结构有助于最简单的可能的可观察:自由能,这是使用复制技巧计算。这与用于计算纠缠熵的复制技巧不同,并且出现在任何广泛量的计算中。我们认为,JT重力和简化版本的CGHS承认一个政权,连接副本虫洞的自由能的贡献大于断开拓扑结构。在这两种理论中,我们都发现了复本对称性破缺的证据,这让人想起某些自旋玻璃的行为。我们从这个角度讨论了在重力系综平均可能的见解。

英文摘要:

Euclidean wormholes -- geometries which connect disconnected boundaries -- present a challenge to a standard quantum mechanical interpretation of the theory. One potential resolution is that the gravitational path integral computes the ensemble average of many theories. The connected topologies contribute to the simplest possible observable: the free energy, which is computed using a replica trick. This is distinct from the replica trick used to compute entanglement entropies, and appears in the computation of any extensive quantity. We argue that both JT gravity and a simplified version of CGHS admit a regime where the contribution of connected replica wormholes to the free energy is larger than that of disconnected topologies. In both theories we find evidence of replica symmetry breaking, which is reminiscent of the behavior of certain spin glasses. We discuss possible insights about ensemble averaging in gravity from this perspective.

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