论文标题
半沃尔孔和合奏平均
Half-Wormholes and Ensemble Averages
论文作者
论文摘要
我们研究了各种集合平均模型中对光谱相关器的“半孔状”马鞍点的贡献，包括各种统计模型，广义的0D SYK模型，1D Brownian Syk模型及其扩展。在统计整体模型中，可以细节研究随机变量的更一般分布，我们发现，当随机变量的分布显着偏离高斯分布时，先前提出的半孔近似值的准确性可以得到改善。我们提出了一种修改后的半孔贡献的近似方案，该方案在这些更一般的理论中也很好地工作。在各种广义的0D SYK模型中，我们确定了新的半孔样鞍点的贡献。在0D SYK模型和1D Brownian Syk模型中，除了虫洞和半孔鞍座外，我们在频谱相关器中发现了新的非平凡的鞍座，这些鞍座可能会提供与琐碎的自我传播鞍座相同顺序的贡献。但是，经过仔细的Lefschetz thimble分析，我们表明不应包括这些非平凡的马鞍。我们还阐明了某些模型中“链接的半沃尔孔”和“未连接半worm孔”之间的区别。
We study "half-wormhole-like" saddle point contributions to spectral correlators in a variety of ensemble average models, including various statistical models, generalized 0d SYK models, 1d Brownian SYK models and an extension of it. In statistical ensemble models, where more general distributions of the random variables could be studied in great details, we find the accuracy of the previously proposed approximation for the half-wormholes could be improved when the distribution of the random variables deviate significantly from Gaussian distributions. We propose a modified approximation scheme of the half-wormhole contributions that also work well in these more general theories. In various generalized 0d SYK models we identify new half-wormhole-like saddle point contributions. In the 0d SYK model and 1d Brownian SYK model, apart from the wormhole and half-wormhole saddles, we find new non-trivial saddles in the spectral correlators that would potentially give contributions of the same order as the trivial self-averaging saddles. However after a careful Lefschetz-thimble analysis we show that these non-trivial saddles should not be included. We also clarify the difference between "linked half-wormholes" and "unlinked half-wormholes" in some models.
