混沌共形场论中的对称性与谱统计 II：Maass尖点形式与算术混沌
Symmetries and spectral statistics in chaotic conformal field theories II: Maass cusp forms and arithmetic chaos
AI总结：
本文研究二维混沌共形场论中谱形因子的随机矩阵普适性，聚焦Maass尖点形式的“算术混沌”统计，证明晚期近极端谱形因子仅依赖其统计平均，并通过引导方法唯一确定线性斜坡对应的谱相关性，其次领头修正与AdS3引力中的虫洞振幅一致。
摘要：
我们继续研究二维共形场论中的随机矩阵普适性。通过在基本域上拉普拉斯算子的模不变本征函数基中展开谱形因子，我们得以进行这一研究。本文关注谱的离散部分，即由Maass尖点形式组成。它们的特征值和傅里叶系数都是零星离散的数字，具有有趣的统计性质以及与解析数论的联系；这被称为“算术混沌”。我们证明，在晚期时刻，近极端的谱形因子仅对这些不规则特征的统计平均敏感。然而，如果所有自旋扇区都表现出普遍的随机矩阵特征值排斥（“线性斜坡”），那么关于其统计分布的完整信息就编码在谱形因子中。我们“引导”了对应于普遍线性斜坡的尖点形式基函数之间的谱相关性，并证明它们在理论依赖的次领头修正之前是唯一的。对尖点形式的统计处理提供了一种以最小方式确定次领头修正的自然途径，我们观察到这导致了与AdS${}_3$引力中[torus]×[interval]虫洞振幅所描述的相同的相关性。
英文摘要：
We continue the study of random matrix universality in two-dimensional conformal field theories. This is facilitated by expanding the spectral form factor in a basis of modular invariant eigenfunctions of the Laplacian on the fundamental domain. The focus of this paper is on the discrete part of the spectrum, which consists of the Maass cusp forms. Both their eigenvalues and Fourier coefficients are sporadic discrete numbers with interesting statistical properties and relations to analytic number theory; this is referred to as `arithmetic chaos'. We show that the near-extremal spectral form factor at late times is only sensitive to a statistical average over these erratic features. Nevertheless, complete information about their statistical distributions is encoded in the spectral form factor if all its spin sectors exhibit universal random matrix eigenvalue repulsion (a `linear ramp'). We `bootstrap' the spectral correlations between the cusp form basis functions that correspond to a universal linear ramp and show that they are unique up to theory-dependent subleading corrections. The statistical treatment of cusp forms provides a natural avenue to fix the subleading corrections in a minimal way, which we observe leads to the same correlations as those described by the [torus]$\times$[interval] wormhole amplitude in AdS${}_3$ gravity.
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