Entanglement renormalization and integral geometry

We revisit the applications of integral geometry in AdS$_3$ and argue that the metric of the kinematic space can be realized as the entanglement contour, which is defined as the additive entanglement density. From the renormalization of the entanglement contour, we can holographically understand the operations of disentangler and isometry in multi-scale entanglement renormalization ansatz. Furthermore, a renormalization group equation of the long-distance entanglement contour is then derived. We then generalize this integral geometric construction to higher dimensions and in particular demonstrate how it works in bulk space of homogeneity and isotropy.Comment: 40 pages, 7 figures. v2: discussions on the general measure added, typos fixed; v3: sections reorganized, various points clarified, to appear in JHE

OPE of the stress tensors and surface operators

We demonstrate that the divergent terms in the OPE of a stress tensor and a surface operator of general shape cannot be constructed only from local geometric data depending only on the shape of the surface. We verify this holographically at d=3 for Wilson line operators or equivalently the twist operator corresponding to computing the entanglement entropy using the Ryu-Takayanagi formula. We discuss possible implications of this result.Comment: 20 pages, no figur

MODELING FRESH ORGANIC PRODUCE CONSUMPTION: A GENERALIZED DOUBLE-HURDLE MODEL APPROACH

Using actual retail data, this study is intended to profile consumers' social economic characteristics related to the growth of the fresh organic produce market with a generalized double-hurdle model. The nested test shows that the above model performs significantly better than Cragg's independent double-hurdle model and Tobit model.Food Consumption/Nutrition/Food Safety,