全息纠缠熵的环面不等式推广框架
A framework for generalizing toric inequalities for holographic entanglement entropy
AI总结：
本文提出了全息纠缠熵中环面不等式的多参数推广猜想，并通过平铺欧几里得空间构建图和利用循环图的图笛卡尔积两种方法扩展了证明，同时验证了特定参数范围内的猜想。
摘要：
我们猜想了一个对 \cite{Czech:2023xed} 中环面不等式的多参数推广。然后我们用两种方式扩展了他们对广义环面不等式的证明方法。第一种扩展通过平铺欧几里得空间构建了对应于环面不等式和广义环面猜想的图。纠缠楔嵌套关系随后决定了这些平铺图形的几何结构。在第二种扩展中，我们利用不等式和猜想的循环性质构建了循环图。然后，该图可以通过循环图的图笛卡尔积获得。此外，我们遵循 \cite{Czech:2023xed} 在图上定义了一组结点。这些带有结点的图随后意味着其相关不等式的有效性。我们研究了图可以分解为环面不相交并集的情况。在这种特定情况下，我们探索并证明了某些参数范围内的猜想。我们还讨论了探索对应几何为 $d$ 维环面 $(d>2)$ 的猜想不等式的方法。
英文摘要：
We conjecture a multi-parameter generalization of the toric inequalities of \cite{Czech:2023xed}. We then extend their proof methods for the generalized toric inequalities in two ways. The first extension constructs the graph corresponding to the toric inequalities and the generalized toric conjectures by tiling the Euclidean space. An entanglement wedge nesting relation then determines the geometric structure of the tiles. In the second extension, we exploit the cyclic nature of the inequalities and conjectures to construct cycle graphs. Then, the graph can be obtained using graph Cartesian products of cycle graphs. In addition, we define a set of knots on the graph by following \cite{Czech:2023xed}. These graphs with knots then imply the validity of their associated inequality. We study the case where the graph can be decomposed into disjoint unions of torii. Under the specific case, we explore and prove the conjectures for some ranges of parameters. We also discuss ways to explore the conjectured inequalities whose corresponding geometries are $d$-dimensional torii $(d>2)$
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