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arXiv 2408.08010hep-thgr-qc
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扰动量子黑洞

Perturbing a quantum black hole

Casey Cartwright, Umut Gürsoy, Juan F. Pedraza, Guim Planella Planas

AI总结:

本文研究 qBTZ 量子黑洞的 QNM、极跳与复动量极点碰撞,揭示量子反作用对弛豫、混沌输运及 Green 函数解析结构的独特影响。

摘要:

我们分析了与量子 Bañados-Teitelboim-Zanelli(qBTZ)黑洞对偶的场论中关联函数的解析结构;qBTZ 是一个膜世界模型,包含来自量子共形物质的精确反作用。我们首先计算了维数为 Δ、自旋为 s=0、±1/2 的算符的准正常模(QNM)谱。主导 QNM 及其泛音根据 qBTZ 解的分支表现出性质上不同的行为,这些分支对应不同的 CFT 态:分支 1 是被视界修饰的锥形奇点,而分支 2 是经量子修正的 BTZ 黑洞。因此,探测物质的弛豫能够有效区分这些 CFT 态并识别相应的体描述。随后,我们转向 Green 函数不唯一的极跳位置。在这些点上,频率与温度成正比,但由于量子效应,动量表现出复杂的温度依赖。在最靠近原点的极跳点反映量子混沌这一假设下,我们推断了对偶理论中量子 Lyapunov 指数和蝴蝶速度可能具有的行为。最后,我们考察了复动量空间中的极点碰撞,表明量子修正在推迟 Green 函数极点的解析结构上留下了独特印记,导致能级交叉现象;这与未经修正的 BTZ 几何中的能级接触现象显著不同。

英文摘要:

We analyze the analytic structure of correlators in the field theory dual to the quantum Bañados-Teitelboim-Zanelli (qBTZ) black hole, a braneworld model incorporating exact backreaction from quantum conformal matter. We first compute the quasi-normal mode (QNM) spectrum of operators with dimension $Δ$ and spin $s=0,\pm 1/2$. The leading QNMs and their overtones display qualitatively different behavior depending on the branch of qBTZ solution, which corresponds to distinct CFT states: branch 1 is a conical singularity dressed with a horizon while branch 2 is a quantum-corrected BTZ black hole. Consequently, the relaxation of probe matter effectively differentiates the CFT states and identifies the corresponding bulk descriptions. We then turn to pole-skipping locations where Green's functions are not unique. At these points, frequency is proportional to temperature, but momentum exhibits complex temperature dependence due to quantum effects. Under the assumption that the pole-skipping point closest to the origin reflects quantum chaos, we infer the likely behavior of the quantum Lyapunov exponent and butterfly velocity in the dual theory. Finally, we examine pole collisions in complex momentum space, showing that quantum corrections imprint a unique signature on the analytic structure of the poles in retarded Green's functions, resulting in level-crossing phenomena that differ notably from the level-touching phenomena in the uncorrected BTZ geometry.

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