近日，美国东北大学的Keiichiro Furuya及其研究团队取得一项新进展。经过不懈努力，他们提出推广全息纠缠熵环面不等式的框架。相关研究成果已于2024年10月31日在国际知名学术期刊《高能物理杂志》上发表。

该研究团队推测了[1]中环面不等式的多参数推广。然后，研究人员从两个方面扩展了这些推广后的环面不等式证明方法。第一个扩展是通过平铺欧几里得空间，构建了对应于环面不等式和推广后的环面猜想的图。接着，一个纠缠楔形嵌套关系决定了这些平铺单元的几何结构。在第二个扩展中，研究人员利用不等式和猜想的循环性质构建了循环图。然后，可以通过循环图的笛卡尔积来获得该图。

此外，研究人员遵循[1]中的方法，在图上定义了一组结点。这些带结点的图随后证明了其相关不等式的有效性。他们研究了图可以分解为不相交环面并集的情况。在这一特定情况下，他们探索并证明了某些参数范围内的猜想。他们还讨论了如何探索那些对应几何为d维环面（d > 2）的猜想不等式。

附：英文原文

Title: A framework for generalizing toric inequalities for holographic entanglement entropy

Author: Bao, Ning, Furuya, Keiichiro, Naskar, Joydeep

Issue&Volume: 2024-10-31

Abstract: We conjecture a multi-parameter generalization of the toric inequalities of [1]. 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 [1]. 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).

DOI: 10.1007/JHEP10(2024)251

Source: https://link.springer.com/article/10.1007/JHEP10(2024)251