96 research outputs found
Quintics with Finite Simple Symmetries
We construct all quintic invariants in five variables with simple Non-Abelian
finite symmetry groups. These define Calabi-Yau three-folds which are left
invariant by the action of A_5, A_6 or PSL_2(11).Comment: 18 pages, typos corrected, matches published versio
Weakly--exceptional quotient singularities
A singularity is said to be weakly--exceptional if it has a unique purely log
terminal blow up. In dimension , V. Shokurov proved that weakly--exceptional
quotient singularities are exactly those of types , , ,
. This paper classifies the weakly--exceptional quotient singularities
in dimensions and
Generalized McKay quivers of rank three
For each finite subgroup G of SL(n, C), we introduce the generalized Cartan
matrix C_{G} in view of McKay correspondence from the fusion rule of its
natural representation. Using group theory, we show that the generalized Cartan
matrices have similar favorable properties such as positive semi-definiteness
as in the classical case of affine Cartan matrices (the case of SL(2,C)). The
complete McKay quivers for SL(3,C) are explicitly described and classified
based on representation theory
G(2) quivers
We present, in explicit matrix representation and a modernity befitting the community, the classification of the finite discrete subgroups of G2 and compute the McKay quivers arising therefrom. Of physical interest are the classes of Script N = 1 gauge theories descending from M-theory and of mathematical interest are possible steps toward a systematic study of crepant resolutions to smooth G2 manifolds as well as generalised McKay Correspondences. This writing is a companion monograph to hep-th/9811183 and hep-th/9905212, wherein the analogues for Calabi-Yau three- and four-folds were considered
SIC~POVMs and Clifford groups in prime dimensions
We show that in prime dimensions not equal to three, each group covariant
symmetric informationally complete positive operator valued measure (SIC~POVM)
is covariant with respect to a unique Heisenberg--Weyl (HW) group. Moreover,
the symmetry group of the SIC~POVM is a subgroup of the Clifford group. Hence,
two SIC~POVMs covariant with respect to the HW group are unitarily or
antiunitarily equivalent if and only if they are on the same orbit of the
extended Clifford group. In dimension three, each group covariant SIC~POVM may
be covariant with respect to three or nine HW groups, and the symmetry group of
the SIC~POVM is a subgroup of at least one of the Clifford groups of these HW
groups respectively. There may exist two or three orbits of equivalent
SIC~POVMs for each group covariant SIC~POVM, depending on the order of its
symmetry group. We then establish a complete equivalence relation among group
covariant SIC~POVMs in dimension three, and classify inequivalent ones
according to the geometric phases associated with fiducial vectors. Finally, we
uncover additional SIC~POVMs by regrouping of the fiducial vectors from
different SIC~POVMs which may or may not be on the same orbit of the extended
Clifford group.Comment: 30 pages, 1 figure, section 4 revised and extended, published in J.
Phys. A: Math. Theor. 43, 305305 (2010
Interacting Preformed Cooper Pairs in Resonant Fermi Gases
We consider the normal phase of a strongly interacting Fermi gas, which can
have either an equal or an unequal number of atoms in its two accessible spin
states. Due to the unitarity-limited attractive interaction between particles
with different spin, noncondensed Cooper pairs are formed. The starting point
in treating preformed pairs is the Nozi\`{e}res-Schmitt-Rink (NSR) theory,
which approximates the pairs as being noninteracting. Here, we consider the
effects of the interactions between the Cooper pairs in a Wilsonian
renormalization-group scheme. Starting from the exact bosonic action for the
pairs, we calculate the Cooper-pair self-energy by combining the NSR formalism
with the Wilsonian approach. We compare our findings with the recent
experiments by Harikoshi {\it et al.} [Science {\bf 327}, 442 (2010)] and
Nascimb\`{e}ne {\it et al.} [Nature {\bf 463}, 1057 (2010)], and find very good
agreement. We also make predictions for the population-imbalanced case, that
can be tested in experiments.Comment: 10 pages, 6 figures, accepted version for PRA, discussion of the
imbalanced Fermi gas added, new figure and references adde
Counting BPS Operators in Gauge Theories: Quivers, Syzygies and Plethystics
We develop a systematic and efficient method of counting single-trace and
multi-trace BPS operators with two supercharges, for world-volume gauge
theories of D-brane probes for both and finite . The
techniques are applicable to generic singularities, orbifold, toric, non-toric,
complete intersections, et cetera, even to geometries whose precise field
theory duals are not yet known. The so-called ``Plethystic Exponential''
provides a simple bridge between (1) the defining equation of the Calabi-Yau,
(2) the generating function of single-trace BPS operators and (3) the
generating function of multi-trace operators. Mathematically, fascinating and
intricate inter-relations between gauge theory, algebraic geometry,
combinatorics and number theory exhibit themselves in the form of plethystics
and syzygies.Comment: 59+1 pages, 7 Figure
Classification of K3-surfaces with involution and maximal symplectic symmetry
K3-surfaces with antisymplectic involution and compatible symplectic actions
of finite groups are considered. In this situation actions of large finite
groups of symplectic transformations are shown to arise via double covers of
Del Pezzo surfaces. A complete classification of K3-surfaces with maximal
symplectic symmetry is obtained.Comment: 26 pages; final publication available at http://www.springerlink.co
Stakeholders, collaboration, food, and wine: The case of Jumillaâs Gastronomic Days
An emerging literature on gastronomic events highlights the growing interest among academics, event organisers and development agencies in identifying potential or actual outcomes from gastronomic events. Partly in response to such interest, this study seeks to contribute to the literature on events management, studying the contribution of various stakeholders involved in the âGastronomic Daysâ of Jumilla, Spain. Semi-structured, face-to-face, in-depth interviews were conducted with the managers and owners of four participating businesses to the event. The data collection was complemented through on-site visits, observations, and interviews with eight other local businesses. The findings underline the significance of collaboration among these participants to grow and sustain the event, as well as voluntary efforts by event âstakeholders.â Importantly, a common objective was identified in the form of enhancing the image of the local products, and overall that of the region, to âconvertâ residents, and also outside consumers and tourists to Jumillaâs products. These findings have significant implications for Jumillaâs community. In particular, the importance and efforts of a regionâs food stakeholders in contributing to adding value and improving the local food culture emerge as useful aspects, with potential benefits for local food growers, hospitality and tourism sectors, and residents
Mutations in GABRB3
Objective: To examine the role of mutations in GABRB3 encoding the b3 subunit of the GABAA receptor in individual patients with epilepsy with regard to causality, the spectrum of genetic variants, their pathophysiology, and associated phenotypes. Methods: We performed massive parallel sequencing of GABRB3 in 416 patients with a range of epileptic encephalopathies and childhood-onset epilepsies and recruited additional patients with epilepsy with GABRB3 mutations from other research and diagnostic programs. Results: We identified 22 patients with heterozygous mutations in GABRB3, including 3 probands frommultiplex families. The phenotypic spectrum of the mutation carriers ranged from simple febrile seizures, genetic epilepsies with febrile seizures plus, and epilepsy withmyoclonic-atonic seizures to West syndrome and other types of severe, early-onset epileptic encephalopathies. Electrophysiologic analysis of 7 mutations in Xenopus laevis oocytes, using coexpression of wild-type or mutant beta(3), together with alpha(5) and gamma(2s) subunits and an automated 2-microelectrode voltage-clamp system, revealed reduced GABA-induced current amplitudes or GABA sensitivity for 5 of 7 mutations. Conclusions: Our results indicate that GABRB3 mutations are associated with a broad phenotypic spectrum of epilepsies and that reduced receptor function causing GABAergic disinhibition represents the relevant disease mechanism
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