2,822 research outputs found
Scaling of entanglement entropy in the (branching) multi-scale entanglement renormalization ansatz
We investigate the scaling of entanglement entropy in both the multi-scale
entanglement renormalization ansatz (MERA) and in its generalization, the
branching MERA. We provide analytical upper bounds for this scaling, which take
the general form of a boundary law with various types of multiplicative
corrections, including power-law corrections all the way to a bulk law. For
several cases of interest, we also provide numerical results that indicate that
these upper bounds are saturated to leading order. In particular we establish
that, by a suitable choice of holographic tree, the branching MERA can
reproduce the logarithmic multiplicative correction of the boundary law
observed in Fermi liquids and spin-Bose metals in dimensions.Comment: 17 pages, 14 figure
Holographic dual of the five-point conformal block
We present the holographic object which computes the five-point global
conformal block in arbitrary dimensions for external and exchanged scalar
operators. This object is interpreted as a weighted sum over infinitely many
five-point geodesic bulk diagrams. These five-point geodesic bulk diagrams
provide a generalization of their previously studied four-point counterparts.
We prove our claim by showing that the aforementioned sum over geodesic bulk
diagrams is the appropriate eigenfunction of the conformal Casimir operator
with the right boundary conditions. This result rests on crucial inspiration
from a much simpler -adic version of the problem set up on the Bruhat-Tits
tree.Comment: 20 pages + references, several figures. v2: Minor typos fixed,
matches published versio
Hawking from Catalan
The Virasoro algebra determines all `graviton' matrix elements in
AdS/CFT. We study the explicit exchange of any number of Virasoro
gravitons between heavy and light CFT operators at large central charge.
These graviton exchanges can be written in terms of new on-shell tree diagrams,
organized in a perturbative expansion in , the heavy operator dimension
divided by the central charge. The Virasoro vacuum conformal block, which is
the sum of all the tree diagrams, obeys a differential recursion relation
generalizing that of the Catalan numbers. We use this recursion relation to sum
the on-shell diagrams to all orders, computing the Virasoro vacuum block.
Extrapolating to large determines the Hawking temperature of a BTZ
black hole in dual AdS theories.Comment: 19+8 pages, 5 figure
Parsing with CYK over Distributed Representations
Syntactic parsing is a key task in natural language processing. This task has
been dominated by symbolic, grammar-based parsers. Neural networks, with their
distributed representations, are challenging these methods. In this article we
show that existing symbolic parsing algorithms can cross the border and be
entirely formulated over distributed representations. To this end we introduce
a version of the traditional Cocke-Younger-Kasami (CYK) algorithm, called
D-CYK, which is entirely defined over distributed representations. Our D-CYK
uses matrix multiplication on real number matrices of size independent of the
length of the input string. These operations are compatible with traditional
neural networks. Experiments show that our D-CYK approximates the original CYK
algorithm. By showing that CYK can be entirely performed on distributed
representations, we open the way to the definition of recurrent layers of
CYK-informed neural networks.Comment: The algorithm has been greatly improved. Experiments have been
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Holograms: The story of a word and its cultural uses
Holograms reached popular consciousness during the 1960s and have since left audiences alternately fascinated, bemused or inspired. Their impact was conditioned by earlier cultural associations and successive reimaginings by wider publics. Attaining peak public visibility during the 1980s, holograms have been found more in our pockets (as identity documents) and in our minds (as video-gaming fantasies and “faux
hologram” performers) than in front of our eyes. The most enduring, popular interpretations of the word “hologram” evoke the traditional allure of magic and galvanize hopeful technological dreams. This article explores the mutating cultural uses of the term “hologram” as marker of magic, modernity and optimism
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