24,393 research outputs found
Holographic Entropy Cone with Time Dependence in Two Dimensions
In holographic duality, if a boundary state has a geometric description that
realizes the Ryu-Takayanagi proposal then its entanglement entropies must obey
certain inequalities that together define the so-called holographic entropy
cone. A large family of such inequalities have been proven under the assumption
that the bulk geometry is static, using a method involving contraction maps. By
using kinematic space techniques, we show that in two boundary (three bulk)
dimensions, all entropy inequalities that can be proven in the static case by
contraction maps must also hold in holographic states with time dependence.Comment: 37 pages, 10 figure
On some varieties associated with trees
This article considers some affine algebraic varieties attached to finite
trees and closely related to cluster algebras. Their definition involves a
canonical coloring of vertices of trees into three colors. These varieties are
proved to be smooth and to admit sometimes free actions of algebraic tori. Some
results are obtained on their number of points over finite fields and on their
cohomology.Comment: 37 pages, 7 figure
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