A Holographic Proof of R\'enyi Entropic Inequalities

We prove R\'enyi entropic inequalities in a holographic setup based on the recent proposal for the holographic formula of R\'enyi entropies when the bulk is stable against any perturbation. Regarding the R\'enyi parameter as an inverse temperature, we reformulate the entropies in analogy with statistical mechanics, which provides us a concise interpretation of the inequalities as the positivities of entropy, energy and heat capacity. This analogy also makes clear a thermodynamic structure in deriving the holographic formula. As a by-product of the proof we obtain a holographic formula to calculate the quantum fluctuation of the modular Hamiltonian. A few examples of the capacity of entanglement are examined in detail.Comment: 29 pages, 1 figure; v3: references added, our assumption for the proof clarifie

Entanglement Entropy of Annulus in Three Dimensions

The entanglement entropy of an annulus is examined in a three-dimensional system with or without a gap. For a free massive scalar field theory, we numerically calculate the mutual information across an annulus. We also study the holographic mutual information in the CGLP background describing a gapped field theory. We discover four types of solutions as the minimal surfaces for the annulus and classify the phase diagrams by varying the inner and outer radii. In both cases, we find the mutual information satisfies the monotonicity dictated by the unitarity and decays exponentially fast as the gap scale is increased. We speculate this is a universal behavior in any gapped system.Comment: 29 pages, 13 figures, v2: references added, minor change

Renormalized Entanglement Entropy on Cylinder

We develop a framework of calculating entanglement entropy for non-conformal field theories with the use of the dilaton effective action. To illustrate it, we locate a theory on a cylinder $\mathbb{R} \times \mathbb{S}^{2}$ and compute entanglement entropy of a cap-like region perturbatively with respect to the mass for a free massive scalar field. A renormalized entanglement entropy (REE) is proposed to regularize the ultraviolet divergence on the cylinder. We find that the REE decreases monotonically both in the small and large mass regions as the mass increases. We confirm all of these behaviors by the numerical calculations, which further shows the monotonic decrease of the REE in the entire renormalization group flow.Comment: 28 pages, 6 figures, v2: a new section on an interesting discrepancy added, some explanations clarifie

Holographic Entanglement and Causal Shadow in Time-Dependent Janus Black Hole

We holographically compute an inter-boundary entanglement entropy in a time-dependent two-sided black hole which was constructed in hep-th/0701108 by applying time-dependent Janus deformation to BTZ black hole. The black hole contains "causal shadow region" which is causally disconnected from both the conformal boundaries. We find that the Janus deformation results in an earlier phase transition between the extremal surfaces and that the phase transition disappears when the causal shadow is sufficiently large.Comment: PDFLaTeX, 1+24 pages, 5 figures, v2: minor changes, accepted by JHE

量子エンタングルメントとホログラフィー

学位の種別: 課程博士審査委員会委員 : （主査）東京大学教授 加藤 光裕, 東京大学准教授 横山 将志, 東京大学教授 堀 健太朗, 東京大学准教授 松尾 泰, 東京大学准教授 大川 祐司University of Tokyo(東京大学

Differences between professionals in treatment planning for patients with stage III lung cancer using treatment-planning QA software

Background: The quality of treatment planning for stage III non-small cell lung cancer varies within and between facilities due to the different professions involved in planning. Dose estimation parameters were calculated using a feasibility dose-volume histogram (FDVH) implemented in the treatment planning quality assurance software PlanIQ. This study aimed to evaluate differences in treatment planning between occupations using manual FDVH-referenced treatment planning to identify their characteristics. Materials and methods: The study included ten patients with stage III non-small cell lung cancer, and volumetric-modulated arc therapy was used as the treatment planning technique. Fifteen planners, comprising five radiation oncologists, five medical physicists, and five radiological technologists, developed treatment strategies after referring to the FDVH. Results: Medical physicists had a higher mean dose at D98% of the planning target volume (PTV) and a lower mean dose at D2% of the PTV than those in other occupations. Medical physicists had the lowest irradiation lung volumes (V5 Gy and V13 Gy) compared to other professions, and radiation oncologists had the lowest V20 Gy and mean lung dose. Radiological technologists had the highest irradiation volumes for dose constraints at all indexes on the normal lung volume. Conclusions: The quality of the treatment plans developed in this study differed between occupations due to their background expertise, even when an FDVH was used as a reference. Therefore, discussing and sharing knowledge and treatment planning techniques among professionals is essential to determine the optimal treatment plan for each facility and patient