2,183 research outputs found
Modave lectures on bulk reconstruction in AdS/CFT
These lecture notes are based on a series of lectures given at the XIII
Modave summer school in mathematical physics. We review the construction due to
Hamilton, Kabat, Lifschytz and Lowe for reconstructing local bulk operators
from CFT operators in the context of AdS/CFT and show how to recover bulk
correlation functions from this definition. Building on the work of these
authors, it has been noted that the bulk displays quantum error correcting
properties. We will discuss tensor network toy models to exemplify these
remarkable features. We will discuss the role of gauge invariance and of
diffeomorphism symmetry in the reconstruction of bulk operators. Lastly, we
provide another method of bulk reconstruction specified to AdS/CFT in
which bulk operators create cross-cap states in the CFT.Comment: 35 pages, 8 figures, lecture notes, v4: a few minor improvements upon
the published proceedings version (version 3 of these lecture notes in arXiv)
have been implemente
Increasing information feed in the process of structural steel design
Research initiatives throughout history have shown how a designer typically makes associations and references to a vast amount of knowledge based on experiences to make decisions. With the increasing usage of information systems in our everyday lives, one might imagine an information system that provides designers access to the ‘architectural memories’ of other architectural designers during the design process, in addition to their own physical architectural memory. In this paper, we discuss how the increased adoption of semantic web technologies might advance this idea. We investigate to what extent information can be described with these technologies in the context of structural steel design. This investigation indicates significant possibilities regarding information reuse in the process of structural steel design and, by extent, in other design contexts as well. However, important obstacles and question remarks can still be outlined as well
Heavy-Heavy-Light-Light correlators in Liouville theory
We compute four-point functions of two heavy and two "perturbatively heavy"
operators in the semiclassical limit of Liouville theory on the sphere. We
obtain these "Heavy-Heavy-Light-Light" (HHLL) correlators to leading order in
the conformal weights of the light insertions in two ways: (a) via a path
integral approach, combining different methods to evaluate correlation
functions from complex solutions for the Liouville field, and (b) via the
conformal block expansion. This latter approach identifies an integral over the
continuum of normalizable states and a sum over an infinite tower of lighter
discrete states, whose contribution we extract by analytically continuing
standard results to our HHLL setting. The sum over this tower reproduces the
sum over those complex saddlepoints of the path integral that contribute to the
correlator. Our path integral computations reveal that when the two light
operators are inserted at equal time in radial quantization, the leading-order
HHLL correlator is independent of their separation, and more generally that at
this order there is no short-distance singularity as the two light operators
approach each other. The conformal block expansion likewise shows that in the
discrete sum short-distance singularities are indeed absent for all
intermediate states that contribute. In particular, the Virasoro vacuum block,
which would have been singular at short distances, is not exchanged. The
separation-independence of equal-time correlators is due to cancelations
between the discrete contributions. These features lead to a Lorentzian
singularity that, in conformal theories with anti-de Sitter (AdS) duals, would
be associated to locality below the AdS scale.Comment: 40 pages, 1 figure; v2: clarifications added, minor typos corrected,
published versio
Ontwikkeling van een Google SketchUp-plugin als ontwerpinstrument voor een energiezuinige architectuur
Sinds 1 januari 2006 is in Vlaanderen de energieprestatieregelgeving van kracht. Vlaamse architecten, ontwerpers en ingenieurs worstelen met deze nieuwe wetgeving en zijn nog steeds op zoek naar een instrument waarmee ze reeds van in de beginfase van het onwerp het peil van energieprestatie kunnen bepalen. Deze paper behandelt het onderzoek naar en de ontwikkeling van een Google SketchUp-plugin, dat kadert in de masterscriptie van Tine Jonckheere. Er werd onderzocht wat de specifieke noden zijn van de architecten in Vlaanderen en welke oplossingen er reeds voorhanden zijn. Vervolgens werd een prototype van de SketchUp-plugin ontwikkeld en getoetst aan de eisen en noden van de architect
Entanglement versus entwinement in symmetric product orbifolds
We study the entanglement entropy of gauged internal degrees of freedom in a
two dimensional symmetric product orbifold CFT, whose configurations consist of
strands sewn together into "long" strings, with wavefunctions symmetrized
under permutations. In earlier work a related notion of "entwinement" was
introduced. Here we treat this system analogously to a system of identical
particles. From an algebraic point of view, we point out that the reduced
density matrix on out of particles is not associated with a subalgebra
of operators, but rather with a linear subspace, which we explain is
sufficient. In the orbifold CFT, we compute the entropy of a single strand in
states holographically dual in the D1/D5 system to a conical defect geometry or
a massless BTZ black hole and find a result identical to entwinement. We also
calculate the entropy of two strands in the state that represents the conical
defect; the result differs from entwinement. In this case, matching entwinement
would require finding a gauge-invariant way to impose continuity across
strands.Comment: 21 pages, v2: short entwinement review section added, and prev.
section 2 rewritten to increase clarity. Matches published versio
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