无知是廉价的：从黑洞熵到QFT的能量最小化态
Ignorance is Cheap: From Black Hole Entropy To Energy-Minimizing States In QFT
摘要：
在某些边缘被捕获的曲面后面，人们可以构造一个几何，它包含一个面积相等但不是更大的极值曲面。这个结构是恩格尔哈特-沃尔将贝肯斯坦-霍金熵解释为粗粒度熵的基础。该构造可以被证明经典地存在，但如果违反了能量守恒条件，则会失败。在这里，我们将粗粒化结构推广到半经典引力。它的有效性是自然的，但我们能够提取一个有趣的非引力极限。我们的建议包含了关于半空间上量子场论态完备化的最小能量的沃尔蚂蚁猜想。它进一步限制了最小能量状态的性质;例如，最小完成能量必须在切割处作为冲击局部化。我们验证了Ceyhan和Faulkner最近的一个明确的建设，这证明了我们的猜想在非引力极限的预测性能。
英文摘要：
Behind certain marginally trapped surfaces one can construct a geometry containing an extremal surface of equal, but not larger area. This construction underlies the Engelhardt-Wall proposal for explaining Bekenstein-Hawking entropy as a coarse-grained entropy. The construction can be proven to exist classically but fails if the Null Energy Condition is violated. Here we extend the coarse-graining construction to semiclassical gravity. Its validity is conjectural, but we are able to extract an interesting nongravitational limit. Our proposal implies Wall's ant conjecture on the minimum energy of a completion of a quantum field theory state on a half-space. It further constrains the properties of the minimum energy state; for example, the minimum completion energy must be localized as a shock at the cut. We verify that the predicted properties hold in a recent explicit construction of Ceyhan and Faulkner, which proves our conjecture in the nongravitational limit.
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