1,483 research outputs found
Monster Anatomy
We investigate the two-dimensional conformal field theories (CFTs) of
, and `dual' to the critical Ising
model, the three state Potts model and the tensor product of two Ising models,
respectively. We argue that these CFTs exhibit moonshines for the double
covering of the baby Monster group, , the triple covering of
the largest Fischer group, and multiple-covering of
the second largest Conway group, . Various
twined characters are shown to satisfy generalized bilinear relations involving
Mckay-Thompson series. We also rediscover that the `self-dual' two-dimensional
bosonic conformal field theory of has the Conway group
as an automorphism group.Comment: 23 pages, revised according to suggestions from JHEP refere
Modular Constraints on Superconformal Field Theories
We constrain the spectrum of and
superconformal field theories in two-dimensions by requiring the NS-NS sector
partition function to be invariant under the congruence
subgroup of the full modular group . We employ semi-definite
programming to find constraints on the allowed spectrum of operators with or
without charges. Especially, the upper bounds on the twist gap for the
non-current primaries exhibit interesting peaks, kinks, and plateau. We
identify a number of candidate rational (S)CFTs realized at the numerical
boundaries and find that they are realized as the solutions to modular
differential equations associated to . Some of the candidate
theories have been discussed by H\"ohn in the context of self-dual extremal
vertex operator (super)algebra. We also obtain bounds for the charged operators
and study their implications to the weak gravity conjecture in AdS.Comment: 50 pages, 16 figure
Modular Constraints on Conformal Field Theories with Currents
We study constraints coming from the modular invariance of the partition
function of two-dimensional conformal field theories. We constrain the spectrum
of CFTs in the presence of holomorphic and anti-holomorphic currents using the
semi-definite programming. In particular, we find the bounds on the twist gap
for the non-current primaries depend dramatically on the presence of
holomorphic currents, showing numerous kinks and peaks. Various rational CFTs
are realized at the numerical boundary of the twist gap, saturating the upper
limits on the degeneracies. Such theories include Wess-Zumino-Witten models for
the Deligne's exceptional series, the Monster CFT and the Baby Monster CFT. We
also study modular constraints imposed by -algebras of various
type and observe that the bounds on the gap depend on the choice of
-algebra in the small central charge region.Comment: 49 pages, 23 figure
Kovalenko's Full-Rank Limit and Overhead as Lower Bounds for Error-Performances of LDPC and LT Codes over Binary Erasure Channels
We present Kovalenko's full-rank limit as a tight lower bound for decoding
error probability of LDPC codes and LT codes over BEC. From the limit, we
derive a full-rank overhead as a lower bound for stable overheads for
successful maximum-likelihood decoding of the codes.Comment: A short version of this paper was presented at ISITA 2008, Auckland
NZ. The first draft was submitted to IEEE Transactions on Information Theory,
2008/0
Generalized gravity model for human migration
The gravity model (GM) analogous to Newton's law of universal gravitation has
successfully described the flow between different spatial regions, such as
human migration, traffic flows, international economic trades, etc. This simple
but powerful approach relies only on the 'mass' factor represented by the scale
of the regions and the 'geometrical' factor represented by the geographical
distance. However, when the population has a subpopulation structure
distinguished by different attributes, the estimation of the flow solely from
the coarse-grained geographical factors in the GM causes the loss of
differential geographical information for each attribute. To exploit the full
information contained in the geographical information of subpopulation
structure, we generalize the GM for population flow by explicitly harnessing
the subpopulation properties characterized by both attributes and geography. As
a concrete example, we examine the marriage patterns between the bride and the
groom clans of Korea in the past. By exploiting more refined geographical and
clan information, our generalized GM properly describes the real data, a part
of which could not be explained by the conventional GM. Therefore, we would
like to emphasize the necessity of using our generalized version of the GM,
when the information on such nongeographical subpopulation structures is
available.Comment: 14 pages, 6 figures, 2 table
Magnetically charged AdS5 black holes from class S theories on hyperbolic 3-manifolds
We study the twisted index of 4d = 2 class S theories on a
closed hyperbolic 3-manifold . Via 6d picture, the index can be written in
terms of topological invariants called analytic torsions twisted by irreducible
flat connections on the 3-manifold. Using the topological expression, we
determine the full perturbative 1/N expansion of the twisted index. The leading
part nicely matches the Bekestein-Hawking entropy of a magnetically charged
black hole in the holographic dual with near-horizon.Comment: 10 pages, v2: minor corrections and references adde
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