On the completeness of contraction map proof method for holographic entropy inequalities

• URL: http://arxiv.org/abs/2506.18086v1
• Date: Sun, 22 Jun 2025 16:21:54 GMT
• Title: On the completeness of contraction map proof method for holographic entropy inequalities
• Authors: Ning Bao, Keiichiro Furuya, Joydeep Naskar,
• Abstract summary: The contraction map proof method is the commonly used method to prove holographic entropy inequalities.<n>In this note, we answer the question in affirmative for all linear holographic entropy inequalities with rational coefficients.<n>We show that, generically, the pre-image of a non-contraction map is not a hypercube, but a proper cubical subgraph.
• Score: 0.10923877073891444
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The contraction map proof method is the commonly used method to prove holographic entropy inequalities. Existence of a contraction map corresponding to a holographic entropy inequality is a sufficient condition for its validity. But is it also necessary? In this note, we answer that question in affirmative for all linear holographic entropy inequalities with rational coefficients. We show that, generically, the pre-image of a non-contraction map is not a hypercube, but a proper cubical subgraph, and show that this manifests as alterations to the geodesic structure in the bulk, which leads to the violation of inequalities by holographic geometries obeying the RT formula.

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