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arXiv 1606.04713hep-thgr-qc
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视界熵满足量子能量猜想吗?

Does horizon entropy satisfy a Quantum Null Energy Conjecture?

Zicao Fu, Donald Marolf

摘要:

事件视界面积给$4G$乘以熵的观点的现代版本是全息场论的Hubeny-Rangamani因果全息信息(CHI)提议。给定全息QFT的区域$R$,CHI计算引力对偶中事件视界的某个切割上的$A/4G$。结果自然地被解释为QFT的粗粒度熵。当$\partial R$位于QFT时空的Killing视界上时,CHI已知比细粒度的Hubeny-Rangamani-Takayanagi(HRT)熵大10倍,并且在这种情况下满足熵的其他非平凡性质。在这里,我们提出的证据表明,它也满足量子零能条件(QNEC),其中的边界的熵的二阶导数的量子场论的一侧的非膨胀的零表面的应力能量通量的表面。特别是,我们显示CHI满足QNEC在1+1全息CFTs时,在状态双锥缺陷在AdS $_3$评估。这一令人惊讶的结果进一步支持了这样一种观点,即CHI定义了一个有用的粗粒度全息熵概念,并暗示了体视界生成器从焦散中出现的速率的前所未有的界限。为了补充我们的动机,我们包括一个附录,推导出相应的粗粒度广义第二定律的1+1全息CFTs微扰耦合到介子引力。

英文摘要:

A modern version of the idea that the area of event horizons gives $4G$ times an entropy is the Hubeny-Rangamani Causal Holographic Information (CHI) proposal for holographic field theories. Given a region $R$ of a holographic QFTs, CHI computes $A/4G$ on a certain cut of an event horizon in the gravitational dual. The result is naturally interpreted as a coarse-grained entropy for the QFT. CHI is known to be finitely greater than the fine-grained Hubeny-Rangamani-Takayanagi (HRT) entropy when $\partial R$ lies on a Killing horizon of the QFT spacetime, and in this context satisfies other non-trivial properties expected of an entropy. Here we present evidence that it also satisfies the quantum null energy condition (QNEC), which bounds the second derivative of the entropy of a quantum field theory on one side of a non-expanding null surface by the flux of stress-energy across the surface. In particular, we show CHI to satisfy the QNEC in 1+1 holographic CFTs when evaluated in states dual to conical defects in AdS$_3$. This surprising result further supports the idea that CHI defines a useful notion of coarse-grained holographic entropy, and suggests unprecedented bounds on the rate at which bulk horizon generators emerge from a caustic. To supplement our motivation, we include an appendix deriving a corresponding coarse-grained generalized second law for 1+1 holographic CFTs perturbatively coupled to dilaton gravity.

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