180 research outputs found
Lusztig limit of quantum sl(2) at root of unity and fusion of (1,p) Virasoro logarithmic minimal models
We introduce a Kazhdan--Lusztig-dual quantum group for (1,p) Virasoro
logarithmic minimal models as the Lusztig limit of the quantum sl(2) at pth
root of unity and show that this limit is a Hopf algebra. We calculate tensor
products of irreducible and projective representations of the quantum group and
show that these tensor products coincide with the fusion of irreducible and
logarithmic modules in the (1,p) Virasoro logarithmic minimal models.Comment: 19 page
Associative algebraic approach to logarithmic CFT in the bulk: the continuum limit of the gl(1|1) periodic spin chain, Howe duality and the interchiral algebra
We develop in this paper the principles of an associative algebraic approach
to bulk logarithmic conformal field theories (LCFTs). We concentrate on the
closed spin-chain and its continuum limit - the symplectic
fermions theory - and rely on two technical companion papers, "Continuum limit
and symmetries of the periodic gl(1|1) spin chain" [Nucl. Phys. B 871 (2013)
245-288] and "Bimodule structure in the periodic gl(1|1) spin chain" [Nucl.
Phys. B 871 (2013) 289-329]. Our main result is that the algebra of local
Hamiltonians, the Jones-Temperley-Lieb algebra JTL_N, goes over in the
continuum limit to a bigger algebra than the product of the left and right
Virasoro algebras. This algebra, S - which we call interchiral, mixes the left
and right moving sectors, and is generated, in the symplectic fermions case, by
the additional field , with
a symmetric form and conformal weights (1,1). We discuss in details
how the Hilbert space of the LCFT decomposes onto representations of this
algebra, and how this decomposition is related with properties of the finite
spin-chain. We show that there is a complete correspondence between algebraic
properties of finite periodic spin chains and the continuum limit. An important
technical aspect of our analysis involves the fundamental new observation that
the action of JTL_N in the spin chain is in fact isomorphic to an
enveloping algebra of a certain Lie algebra, itself a non semi-simple version
of . The semi-simple part of JTL_N is represented by ,
providing a beautiful example of a classical Howe duality, for which we have a
non semi-simple version in the full JTL image represented in the spin-chain. On
the continuum side, simple modules over the interchiral algebra S are
identified with "fundamental" representations of .Comment: 69 pp., 10 figs, v2: the paper has been substantially modified - new
proofs, new refs, new App C with inductive limits construction, et
Kazhdan-Lusztig equivalence and fusion of Kac modules in Virasoro logarithmic models
The subject of our study is the Kazhdan-Lusztig (KL) equivalence in the
context of a one-parameter family of logarithmic CFTs based on Virasoro
symmetry with the (1,p) central charge. All finite-dimensional indecomposable
modules of the KL-dual quantum group - the "full" Lusztig quantum sl(2) at the
root of unity - are explicitly described. These are exhausted by projective
modules and four series of modules that have a functorial correspondence with
any quotient or a submodule of Feigin-Fuchs modules over the Virasoro algebra.
Our main result includes calculation of tensor products of any pair of the
indecomposable modules. Based on the Kazhdan-Lusztig equivalence between
quantum groups and vertex-operator algebras, fusion rules of Kac modules over
the Virasoro algebra in the (1,p) LCFT models are conjectured.Comment: 40pp. V2: a new introduction, corrected typos, some explanatory
comments added, references adde
100 ancient genomes show repeated population turnovers in Neolithic Denmark.
Major migration events in Holocene Eurasia have been characterized genetically at broad regional scales <sup>1-4</sup> . However, insights into the population dynamics in the contact zones are hampered by a lack of ancient genomic data sampled at high spatiotemporal resolution <sup>5-7</sup> . Here, to address this, we analysed shotgun-sequenced genomes from 100 skeletons spanning 7,300 years of the Mesolithic period, Neolithic period and Early Bronze Age in Denmark and integrated these with proxies for diet ( <sup>13</sup> C and <sup>15</sup> N content), mobility ( <sup>87</sup> Sr/ <sup>86</sup> Sr ratio) and vegetation cover (pollen). We observe that Danish Mesolithic individuals of the Maglemose, Kongemose and Ertebølle cultures form a distinct genetic cluster related to other Western European hunter-gatherers. Despite shifts in material culture they displayed genetic homogeneity from around 10,500 to 5,900 calibrated years before present, when Neolithic farmers with Anatolian-derived ancestry arrived. Although the Neolithic transition was delayed by more than a millennium relative to Central Europe, it was very abrupt and resulted in a population turnover with limited genetic contribution from local hunter-gatherers. The succeeding Neolithic population, associated with the Funnel Beaker culture, persisted for only about 1,000 years before immigrants with eastern Steppe-derived ancestry arrived. This second and equally rapid population replacement gave rise to the Single Grave culture with an ancestry profile more similar to present-day Danes. In our multiproxy dataset, these major demographic events are manifested as parallel shifts in genotype, phenotype, diet and land use
Modern temporal network theory: A colloquium
The power of any kind of network approach lies in the ability to simplify a
complex system so that one can better understand its function as a whole.
Sometimes it is beneficial, however, to include more information than in a
simple graph of only nodes and links. Adding information about times of
interactions can make predictions and mechanistic understanding more accurate.
The drawback, however, is that there are not so many methods available, partly
because temporal networks is a relatively young field, partly because it more
difficult to develop such methods compared to for static networks. In this
colloquium, we review the methods to analyze and model temporal networks and
processes taking place on them, focusing mainly on the last three years. This
includes the spreading of infectious disease, opinions, rumors, in social
networks; information packets in computer networks; various types of signaling
in biology, and more. We also discuss future directions.Comment: Final accepted versio
On the mechanisms governing gas penetration into a tokamak plasma during a massive gas injection
A new 1D radial fluid code, IMAGINE, is used to simulate the penetration of gas into a tokamak plasma during a massive gas injection (MGI). The main result is that the gas is in general strongly braked as it reaches the plasma, due to mechanisms related to charge exchange and (to a smaller extent) recombination. As a result, only a fraction of the gas penetrates into the plasma. Also, a shock wave is created in the gas which propagates away from the plasma, braking and compressing the incoming gas. Simulation results are quantitatively consistent, at least in terms of orders of magnitude, with experimental data for a D 2 MGI into a JET Ohmic plasma. Simulations of MGI into the background plasma surrounding a runaway electron beam show that if the background electron density is too high, the gas may not penetrate, suggesting a possible explanation for the recent results of Reux et al in JET (2015 Nucl. Fusion 55 093013)
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