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arXiv 1906.07192hep-thgr-qc
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自由场论启发的AdS黑洞的一个新能量上界

A new energy upper bound for AdS black holes inspired by free field theory

Krai Cheamsawat, Gary Gibbons, Toby Wiseman

摘要:

考虑具有负宇宙学常数的四维引力场的环面紧化平面AdS-Schwarzschild解。它有一个平坦的环面共形边界度量。我们表明,如果空间部分的边界度规是变形的,保持静态和温度和面积固定,然后假设一个静态的体解存在,其能量小于AdS-Schwarzschild解决方案。证明是非微扰的度量变形。虽然我们期望相同的持有自由能的黑洞解,我们到目前为止还不能证明它。在AdS-CFT的上下文中,这意味着一个3维全息CFT上的平面空间环面的体积对偶是AdS-Schwarzschild有一个更大的能量比如果空间几何形状变形的任何方式,保持温度和面积。这项工作的灵感来自于自由场论的先前结果,其中三维空间中的标量和费米子已被证明在能量上不赞成平坦空间。

英文摘要:

We consider the toroidally compactified planar AdS-Schwarzschild solution to 4-dimensional gravity with negative cosmological constant. This has a flat torus conformal boundary metric. We show that if the spatial part of the boundary metric is deformed, keeping it static and the temperature and area fixed, then assuming a static bulk solution exists, its energy is less than that of the AdS-Schwarzschild solution. The proof is non-perturbative in the metric deformation. While we expect the same holds for the free energy for black hole solutions we are so far are not able to prove it. In the context of AdS-CFT this implies a 3-dimensional holographic CFT on a flat spatial torus whose bulk dual is AdS-Schwarzschild has a greater energy than if the spatial geometry is deformed in any way that preserves temperature and area. This work was inspired by previous results in free field theory, where scalars and fermions in 3-dimensions have been shown to energetically disfavour flat space.

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