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 $2$, V. Shokurov proved that weakly--exceptional quotient singularities are exactly those of types $D_{n}$, $E_{6}$, $E_{7}$, $E_{8}$. This paper classifies the weakly--exceptional quotient singularities in dimensions $3$ and $4$

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 $N$ D-brane probes for both $N \to \infty$ and finite $N$. 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 Jumilla’s 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 ‘Gastronomic Days’ 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 ‘stakeholders.’ Importantly, a common objective was identified in the form of enhancing the image of the local products, and overall that of the region, to ‘convert’ residents, and also outside consumers and tourists to Jumilla’s products. These findings have significant implications for Jumilla’s community. In particular, the importance and efforts of a region’s 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