A framework for generalizing toric inequalities for holographic entanglement entropy

• URL: http://arxiv.org/abs/2408.04741v1
• Date: Thu, 8 Aug 2024 19:51:23 GMT
• Title: A framework for generalizing toric inequalities for holographic entanglement entropy
• Authors: Ning Bao, Keiichiro Furuya, Joydeep Naskar,
• Abstract summary: We conjecture and prove a generalization of the toric inequalities of citeCzech:2023xed for some range of parameters. We extend their proof methods for the generalized toric inequalities in two ways.
• Score: 0.10923877073891444
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We conjecture and prove a multi-parameter generalization of the toric inequalities of \cite{Czech:2023xed} for some range of parameters. In addition, we 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 particular case where the graph can be decomposed into disjoint unions of torii. %We extend and propopse the proof by a contraction map of toric inequalities to the conjectures. We also discuss ways to explore the conjectured inequalities whose corresponding geometries are $d$-dimensional torus $(d>2)$.

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