22,286 research outputs found
Explicit Construction of Spin 4 Casimir Operator in the Coset Model
We generalize the Goddard-Kent-Olive (GKO) coset construction to the
dimension 5/2 operator for and compute the fourth order
Casimir invariant in the coset model with the generic unitary minimal
series that can be viewed as perturbations of the
limit, which has been investigated previously in the realization of
free fermion model.Comment: 11 page
M2-brane Perspective on N=6 Super Chern-Simons Theory at Level k
Recently, O. Aharony, O. Bergman, D. L. Jafferis and J. Maldacena (ABJM)
proposed three-dimensional super Chern-Simons-matter theory, which at level k
is supposed to describe the low energy limit of N M2-branes. For large N and k,
but fixed 't Hooft coupling \lambda=N/k, it is dual to type IIA string theory
on AdS_4 x CP^3. For large N but finite k, it is dual to M theory on AdS_4 x
S^7/Z_k. In this paper, relying on the second duality, we find exact giant
magnon and single spike solutions of membrane configurations on AdS_4 x S^7/Z_k
by reducing the system to the Neumann-Rosochatius integrable model. We derive
the dispersion relations and their finite-size corrections with explicit
dependence on the level k.Comment: 19 pages, References adde
Link communities reveal multiscale complexity in networks
Networks have become a key approach to understanding systems of interacting
objects, unifying the study of diverse phenomena including biological organisms
and human society. One crucial step when studying the structure and dynamics of
networks is to identify communities: groups of related nodes that correspond to
functional subunits such as protein complexes or social spheres. Communities in
networks often overlap such that nodes simultaneously belong to several groups.
Meanwhile, many networks are known to possess hierarchical organization, where
communities are recursively grouped into a hierarchical structure. However, the
fact that many real networks have communities with pervasive overlap, where
each and every node belongs to more than one group, has the consequence that a
global hierarchy of nodes cannot capture the relationships between overlapping
groups. Here we reinvent communities as groups of links rather than nodes and
show that this unorthodox approach successfully reconciles the antagonistic
organizing principles of overlapping communities and hierarchy. In contrast to
the existing literature, which has entirely focused on grouping nodes, link
communities naturally incorporate overlap while revealing hierarchical
organization. We find relevant link communities in many networks, including
major biological networks such as protein-protein interaction and metabolic
networks, and show that a large social network contains hierarchically
organized community structures spanning inner-city to regional scales while
maintaining pervasive overlap. Our results imply that link communities are
fundamental building blocks that reveal overlap and hierarchical organization
in networks to be two aspects of the same phenomenon.Comment: Main text and supplementary informatio
Comment on "Exposed-Key Weakness of Alpha-Eta" [Phys. Lett. A 370 (2007) 131]
We show that the insecurity claim of the AlphaEta cryptosystem made by C. Ahn
and K. Birnbaum in Phys. Lett. A 370 (2007) 131-135 under heterodyne attack is
based on invalid extrapolations of Shannon's random cipher analysis and on an
invalid statistical independence assumption. We show, both for standard ciphers
and AlphaEta, that expressions of the kind given by Ahn and Birnbaum can at
best be interpreted as security lower bounds.Comment: Published versio
Robustness and modular structure in networks
Complex networks have recently attracted much interest due to their
prevalence in nature and our daily lives [1, 2]. A critical property of a
network is its resilience to random breakdown and failure [3-6], typically
studied as a percolation problem [7-9] or by modeling cascading failures
[10-12]. Many complex systems, from power grids and the Internet to the brain
and society [13-15], can be modeled using modular networks comprised of small,
densely connected groups of nodes [16, 17]. These modules often overlap, with
network elements belonging to multiple modules [18, 19]. Yet existing work on
robustness has not considered the role of overlapping, modular structure. Here
we study the robustness of these systems to the failure of elements. We show
analytically and empirically that it is possible for the modules themselves to
become uncoupled or non-overlapping well before the network disintegrates. If
overlapping modular organization plays a role in overall functionality,
networks may be far more vulnerable than predicted by conventional percolation
theory.Comment: 14 pages, 9 figure
Electron energy-loss spectrometry on lithiated graphite
Transmission electron energy-loss spectrometry was used to investigate the electronic states of metallic Li and LiC6, which is the Li-intercalated graphite used in Li-ion batteries. The Li K edges of metallic Li and LiC6 were nearly identical, and the C K edges were only weakly affected by the presence of Li. These results suggest only a small charge transfer from Li to C in LiC6, contrary to prior results from surface spectra obtained by x-ray photoelectron spectroscopy. Effects of radiation damage and sample oxidation in the transmission electron microscopy are also reported
The Operator Product Expansion of the Lowest Higher Spin Current at Finite N
For the N=2 Kazama-Suzuki(KS) model on CP^3, the lowest higher spin current
with spins (2, 5/2, 5/2,3) is obtained from the generalized GKO coset
construction. By computing the operator product expansion of this current and
itself, the next higher spin current with spins (3, 7/2, 7/2, 4) is also
derived. This is a realization of the N=2 W_{N+1} algebra with N=3 in the
supersymmetric WZW model. By incorporating the self-coupling constant of lowest
higher spin current which is known for the general (N,k), we present the
complete nonlinear operator product expansion of the lowest higher spin current
with spins (2, 5/2, 5/2, 3) in the N=2 KS model on CP^N space. This should
coincide with the asymptotic symmetry of the higher spin AdS_3 supergravity at
the quantum level. The large (N,k) 't Hooft limit and the corresponding
classical nonlinear algebra are also discussed.Comment: 62 pages; the footnotes added, some redundant appendices removed, the
presentations in the whole paper improved and to appear in JHE
The Primary Spin-4 Casimir Operators in the Holographic SO(N) Coset Minimal Models
Starting from SO(N) current algebra, we construct two lowest primary higher
spin-4 Casimir operators which are quartic in spin-1 fields. For N is odd, one
of them corresponds to the current in the WB_{\frac{N-1}{2}} minimal model. For
N is even, the other corresponds to the current in the WD_{\frac{N}{2}} minimal
model. These primary higher spin currents, the generators of wedge subalgebra,
are obtained from the operator product expansion of fermionic (or bosonic)
primary spin-N/2 field with itself in each minimal model respectively. We
obtain, indirectly, the three-point functions with two real scalars, in the
large N 't Hooft limit, for all values of the 't Hooft coupling which should be
dual to the three-point functions in the higher spin AdS_3 gravity with matter.Comment: 65 pages; present the main results only and to appear in JHEP where
one can see the Appendi
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