论文标题
在大$ q $耦合的Syk模型中营救一个黑洞
Rescuing a black hole in the large-$q$ coupled SYK model
论文作者
论文摘要
在本文中，我们为Sachdev-ye-Kitaev（Syk）模型的两个副本开发了一种一般有效的理论，该副本具有时间依赖性双线性耦合。对于量子淬灭的问题，具有热菲尔德双状态的初始状态，我们展示了系统的演变是如何通过具有经典哈密顿量的复杂的重新训练场来描述的。我们研究该系统中的相关功能，并将大型Q $理论与大量低能效率理论进行比较。特别是，我们研究了``救出的黑洞''的特殊情况，该案例描述了时间发展的热菲尔德双状态如何通过经过仔细调整的时间依赖性耦合来演变为耦合SYK模型的基态。在低能区域，有一个全息双重解释，它是从永恒的黑洞到全球广告$ _2 $ _2 $ vacuum的几何形状。这种几何形状家族使我们能够进入无救援过程的黑洞内部的散装区域。通过比较大$ Q $和低能理论，我们发现，即使在低能区域，如果救援过程开始迟到，则不能忽略与低能理论的偏差。这提供了证据，表明散装的低能量有效理论在黑洞的内部地平线附近失败。我们注意到与高维黑洞奇异性的二维类似物连接的可能性。
In this paper, we develop a general effective theory for two copies of the Sachdev-Ye-Kitaev (SYK) model with a time-dependent bilinear coupling. For a quantum quench problem with an initial state of the thermofield double state, we show how the evolution of the system is described by a complex reparametrization field with a classical Hamiltonian. We study correlation functions in this system and compare the large-$q$ theory with the bulk low energy effective theory. In particular, we study the special case of a ``rescued black hole'', which describes how a time-evolved thermofield double state can evolve to the ground state of a coupled SYK model by a carefully tuned time-dependent coupling. In the low energy region, there is a holographic dual interpretation, which is a geometry that crosses over from an eternal black hole to a global AdS$_2$ vacuum. This family of geometries allow us to access the bulk region that would be the black hole interior without the rescue process. By comparing the large-$q$ and low energy theory, we find that even in the low energy region the deviation from the low energy theory cannot be neglected if the rescue process starts late. This provides evidence that the low energy effective theory of the bulk fails near the inner horizon of the black hole. We note the possibility of a connection to a two-dimensional analog of the higher-dimensional black hole singularity.
