标题： 极小极大曲面和全息熵锥 显示英文标题

标题： Minimax surfaces and the holographic entropy cone

摘要： 我们研究并证明了HRT全息纠缠熵公式的极小极大公式性质，该公式涉及在类时超曲面或时间片上找到最大面积的表面，然后在时间片的选择中进行最小化。 在这种表述中，同调条件是在时空层面施加的：同调区域是时空体积而不是空间区域。 我们特别证明了最小的极小极大同调区域是纠缠楔形。 极小极大方案提出了一种为时间依赖态构建图模型的方法，在该加权图上，最小割计算HRT熵。 图模型的存在将意味着HRT熵遵循与RT熵相同的不等式，换句话说，RT和HRT熵锥体是一致的。 我们构建图模型依赖于时间片满足某种“协作”性质，我们在一些例子中证明了这一点，并给出了部分证明；然而，我们也发现了可能失败的情况。 显示英文摘要

摘要： We study and prove properties of the minimax formulation of the HRT holographic entanglement entropy formula, which involves finding the maximal-area surface on a timelike hypersurface, or time-sheet, and then minimizing over the choice of time-sheet. In this formulation, the homology condition is imposed at the level of the spacetime: the homology regions are spacetime volumes rather spatial regions. We show in particular that the smallest minimax homology region is the entanglement wedge. The minimax prescription suggests a way to construct a graph model for time-dependent states, a weighted graph on which min cuts compute HRT entropies. The existence of a graph model would imply that HRT entropies obey the same inequalities as RT entropies, in other words that the RT and HRT entropy cones coincide. Our construction of a graph model relies on the time-sheets obeying a certain ``cooperating'' property, which we show holds in some examples and for which we give a partial proof; however, we also find scenarios where it may fail.