A relation between moduli space of D-branes on orbifolds and Ising model

We study D-branes transverse to an abelian orbifold C^3/Z_n Z_n. The moduli space of the gauge theory on the D-branes is analyzed by combinatorial calculation based on toric geometry. It is shown that the calculation is related to a problemto count the number of ground states of an antiferromagnetic Ising model. The lattice on which the Ising model is defined is a triangular one defined on the McKay quiver of the orbifold.Comment: 20 pages, 13 figure

Charges of Exceptionally Twisted Branes

The charges of the exceptionally twisted (D4 with triality and E6 with charge conjugation) D-branes of WZW models are determined from the microscopic/CFT point of view. The branes are labeled by twisted representations of the affine algebra, and their charge is determined to be the ground state multiplicity of the twisted representation. It is explicitly shown using Lie theory that the charge groups of these twisted branes are the same as those of the untwisted ones, confirming the macroscopic K-theoretic calculation. A key ingredient in our proof is that, surprisingly, the G2 and F4 Weyl dimensions see the simple currents of A2 and D4, respectively.Comment: 19 pages, 2 figures, LaTex2e, complete proofs of all statements, updated bibliograph

Fractional two-branes, toric orbifolds and the quantum McKay correspondence

We systematically study and obtain the large-volume analogues of fractional two-branes on resolutions of orbifolds C^3/Z_n. We study a generalisation of the McKay correspondence proposed in hep-th/0504164 called the quantum McKay correspondence by constructing duals to the fractional two-branes. Details are explicitly worked out for two examples -- the crepant resolutions of C^3/Z_3 and C^3/Z_5.Comment: 34 pages, 2 figures, LaTeX (JHEP3 style); (v2) typos corrected; (v3) sec 3 reorganise

A-D-E Quivers and Baryonic Operators

We study baryonic operators of the gauge theory on multiple D3-branes at the tip of the conifold orbifolded by a discrete subgroup Gamma of SU(2). The string theory analysis predicts that the number and the order of the fixed points of Gamma acting on S^2 are directly reflected in the spectrum of baryonic operators on the corresponding quiver gauge theory constructed from two Dynkin diagrams of the corresponding type. We confirm the prediction by developing techniques to enumerate baryonic operators of the quiver gauge theory which includes the gauge groups with different ranks. We also find that the Seiberg dualities act on the baryonic operators in a non-Abelian fashion.Comment: 46 pages, 17 figures; v2: minor corrections, note added in section 1, references adde

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

Incidence and risk factors for injury in non-elite netball.

This paper identifies the risk and protective factors for injury in non-elite netball. Three hundred and sixty eight non-elite netballers completed a baseline questionnaire at the commencement of the 1997 preseason. Participants were telephoned each month during the 1997 and 1998 playing seasons to provide details of their exposure at training and games and any injury experiences in the previous four weeks. The incidence of injury in this study was 14 injuries per 1000 player hours. The risk factors for injury were identified as: not warming up before a game (IRR 1.11, 95% CI 1.00 - 1.23) and not being open to new ideas (IRR 1.04, 95% CI 1.00 - 1.07). Training for four or more hours per week (IRR 0.66, 95% CI 0.45 - 0.98) and not sustaining an injury in the previous 12 months (IRR 0.58, 95% CI 0.43 - 0.79) were found to be protective against injury. The risk and protective factors for injury identified in this study can be used as the basis for the development of evidence-based injury prevention strategies that seek to reduce the risk of injury in sport. Injury prevention strategies should focus on the development of effective training programs that include netball-specific skills, activities and movements. Further investigation into the mechanisms associated with the risk and protective factors identified would provide further understanding of why these factors increase or decrease the risk of injury

Bounds on Four-Fermion Contact Interactions Induced by String Resonances

Based on tree-level open-string scattering amplitudes in the low string-scale scenario, we derive the massless fermion scattering amplitudes. The amplitudes are required to reproduce those of the Standard Model at tree level in the low energy limit. We then obtain four-fermion contact interactions by expanding in inverse powers of the string scale and explore the constraints on the string scale from low energy data. The Chan-Paton factors and the string scale are treated as free parameters. We find that data from the neutral and charged current processes at HERA, Drell-Yan process at the Tevatron, and from LEP-II put lower bounds on the string scale M_S >= 0.9-1.3 TeV for typical values of the Chan-Paton factors, which are comparable to Tevatron bounds on Z' and W' masses.Comment: 13 pages, 1 ps figure, version to appear in PR

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

Supersymmetric Gauge Theories, Intersecting Branes and Free Fermions

We show that various holomorphic quantities in supersymmetric gauge theories can be conveniently computed by configurations of D4-branes and D6-branes. These D-branes intersect along a Riemann surface that is described by a holomorphic curve in a complex surface. The resulting I-brane carries two-dimensional chiral fermions on its world-volume. This system can be mapped directly to the topological string on a large class of non-compact Calabi-Yau manifolds. Inclusion of the string coupling constant corresponds to turning on a constant B-field on the complex surface, which makes this space non-commutative. Including all string loop corrections the free fermion theory is elegantly formulated in terms of holonomic D-modules that replace the classical holomorphic curve in the quantum case.Comment: 67 pages, 6 figure

FGF receptor genes and breast cancer susceptibility: results from the Breast Cancer Association Consortium

Background:Breast cancer is one of the most common malignancies in women. Genome-wide association studies have identified FGFR2 as a breast cancer susceptibility gene. Common variation in other fibroblast growth factor (FGF) receptors might also modify risk. We tested this hypothesis by studying genotyped single-nucleotide polymorphisms (SNPs) and imputed SNPs in FGFR1, FGFR3, FGFR4 and FGFRL1 in the Breast Cancer Association Consortium. Methods:Data were combined from 49 studies, including 53 835 cases and 50 156 controls, of which 89 050 (46 450 cases and 42 600 controls) were of European ancestry, 12 893 (6269 cases and 6624 controls) of Asian and 2048 (1116 cases and 932 controls) of African ancestry. Associations with risk of breast cancer, overall and by disease sub-type, were assessed using unconditional logistic regression. Results:Little evidence of association with breast cancer risk was observed for SNPs in the FGF receptor genes. The strongest evidence in European women was for rs743682 in FGFR3; the estimated per-allele odds ratio was 1.05 (95 confidence interval=1.02-1.09, P=0.0020), which is substantially lower than that observed for SNPs in FGFR2. Conclusion:Our results suggest that common variants in the other FGF receptors are not associated with risk of breast cancer to the degree observed for FGFR2. © 2014 Cancer Research UK