标题： 高维Floquet共形场论的动力学相 显示英文标题

标题： Dynamical Phases of Higher Dimensional Floquet CFTs

摘要： 本文研究了时空维度大于二维的 Floquet 共形场论（CFTs）的动力学相。基于我们之前的工作[1]，该工作引入四元数表示法来研究高维 CFTs 中的 Floquet 动力学，我们现在探索更为一般的方波驱动协议，这些协议超越了单一的 SU(1,1) 子群。我们证明，对于多步驱动协议，系统表现出不同的动力学相，这些相由单个周期内表示时间演化的四元数矩阵的本征值性质决定，从而导致不同的驻波响应。我们的分析建立了基本的几何解释，其中这些动力学相直接对应于 CFT 的基空间以及其假设的对偶所居住的更高维 AdS 空间中是否存在 Killing 事件视界。加热相与非极端事件视界相关，临界相与消失于非加热相中的极端事件视界相关。我们在不同参数范围内发展了摄动方法来计算 Floquet Hamiltonian，并展示了如何通过调节驱动参数产生事件视界，从而提供了理解受驱共形系统中加热现象的几何框架。 显示英文摘要

摘要： This paper investigates the dynamical phases of Floquet Conformal Field Theories (CFTs) in space-time dimensions greater than two. Building upon our previous work [1] which introduced quaternionic representations for studying Floquet dynamics in higher-dimensional CFTs, we now explore more general square pulse drive protocols that go beyond a single SU(1,1) subgroup. We demonstrate that, for multi-step drive protocols, the system exhibits distinct dynamical phases characterized by the nature of the eigenvalues of the quaternionic matrix representing time evolution in a single cycle, leading to different stroboscopic responses. Our analysis establishes a fundamental geometric interpretation where these dynamical phases directly correspond to the presence or absence of Killing horizons in the base space of the CFT and in a higher dimensional AdS space on which a putative dual lives. The heating phase is associated with a non-extremal horizon, the critical phase with an extremal horizon which disappears in the non heating phase. We develop perturbative approaches to compute the Floquet Hamiltonians in different regimes and show, how tuning drive parameters can lead to horizons, providing a geometric framework for understanding heating phenomena in driven conformal systems.