SQCD: A Geometric Apercu

We take new algebraic and geometric perspectives on the old subject of SQCD. We count chiral gauge invariant operators using generating functions, or Hilbert series, derived from the plethystic programme and the Molien-Weyl formula. Using the character expansion technique, we also see how the global symmetries are encoded in the generating functions. Equipped with these methods and techniques of algorithmic algebraic geometry, we obtain the character expansions for theories with arbitrary numbers of colours and flavours. Moreover, computational algebraic geometry allows us to systematically study the classical vacuum moduli space of SQCD and investigate such structures as its irreducible components, degree and syzygies. We find the vacuum manifolds of SQCD to be affine Calabi-Yau cones over weighted projective varieties.Comment: 49 pages, 1 figur

Mastering the Master Space

Supersymmetric gauge theories have an important but perhaps under-appreciated notion of a master space, which controls the full moduli space. For world-volume theories of D-branes probing a Calabi-Yau singularity X the situation is particularly illustrative. In the case of one physical brane, the master space F is the space of F-terms and a particular quotient thereof is X itself. We study various properties of F which encode such physical quantities as Higgsing, BPS spectra, hidden global symmetries, etc. Using the plethystic program we also discuss what happens at higher number N of branes. This letter is a summary and some extensions of the key points of a longer companion paper arXiv:0801.1585.Comment: 10 pages, 1 Figur

Sampling Weed Spatial Variability on a Fieldwide Scale

Site-specific weed management recommendations require knowledge of weed species, density, and location in the field. This study compared several sampling techniques to estimate weed density and distribution in two 65-ha no-till Zea mays–Glycine max rotation fields in eastern South Dakota. The most common weeds (Setaria viridis, Setaria glauca, Cirsium arvense, Ambrosia artemisiifolia, and Polygonum pensylvanicum) were counted by species in 0.1-m2 areas on a 15- by 30-m (1,352 points in each field) or 30- by 30-m (676 points in each field) grid pattern, and points were georeferenced and data spatially analyzed. Using different sampling approaches, weed populations were estimated by resampling the original data set. The average density for each technique was calculated and compared with the average field density calculated from the all-point data. All weeds had skewed population distributions with more than 60% of sampling points lacking the specific weed, but very high densities (i.e., \u3e 100 plants m−2) were also observed. More than 300 random samples were required to estimate densities within 20% of the all-point means about 60% of the time. Sampling requirement increased as average density decreased. The W pattern produced average species densities that often were similar to the field averages, but information on patch location was absent. Weed counts taken on the 15- by 30-m grid were dependent spatially and weed contour maps were developed. Kriged maps presented both density and location of weed patches and could be used to establish management zones. However, grid-sampling production fields on a small enough scale to obtain spatially dependent data may have limited usefulness because of time, cost, and labor constraints

Emerging Non-Anomalous Baryonic Symmetries in the AdS_5/CFT_4 Correspondence

We study the breaking of baryonic symmetries in the AdS_5/CFT_4 correspondence for D3 branes at Calabi-Yau three-fold singularities. This leads, for particular VEVs, to the emergence of non-anomalous baryonic symmetries during the renormalization group flow. We claim that these VEVs correspond to critical values of the B-field moduli in the dual supergravity backgrounds. We study in detail the C^3/Z_3 orbifold, the cone over F_0 and the C^3/Z_5 orbifold. For the first two examples, we study the dual supergravity backgrounds that correspond to the breaking of the emerging baryonic symmetries and identify the expected Goldstone bosons and global strings in the infra-red. In doing so we confirm the claim that the emerging symmetries are indeed non-anomalous baryonic symmetries.Comment: 65 pages, 15 figures;v2: minor changes, published versio

Laboratory Tests to Assess Optimal Agricultural Residue Traits for an Abrasive Weed Control System

International Conference of Agricultural Engineering Aarhus, Denmark 26 - 29 June (2016)One of the biggest challenges to organic agricultural production and herbicide resistant crops in industrialized countries today is the non-chemical control of weed plants. Studies of new tools and methods for weed control have been motivated by an increased consumer demand for organic produce and consumer and regulatory demands for a reduction in environmentally harmful herbicide use. The objective of this study is to assess different agricultural residues as gritty weed-abrading materials that are delivered through condensed-air machinery. This is a new weed control technology based on highly-directed air-propelled, innocuous, abrasive grit. Laboratory equipment was designed to calculate the angle of repose of seven different agricultural residues (crushed olive seed, walnut shell, maize cob, poultry manure, soybean seed, almond shell and grape seed). Color, digital, high-speed computer vision analysis of the motion and energy of the air-propelled particles was conducted. The high-speed video analysis determined the capability of each grit to damage a reference surface and kill weeds (species of Amaranthus, Centaurea, and Chenopodium) at different growth stages. A preliminary laboratory trial showed that walnut shell grit has great potential to damage/break the reference surface when it was propelled at 600, 700 and 800 kPa air pressure. Abrasive-weeding reduced final weed biomass by 80% compared with the weedy control at early growth stages. Field research tests are needed in different cropping systems to improve the technical and economic efficiency of this novel system before on-farm adoption

M2-Branes and Fano 3-folds

A class of supersymmetric gauge theories arising from M2-branes probing Calabi-Yau 4-folds which are cones over smooth toric Fano 3-folds is investigated. For each model, the toric data of the mesonic moduli space is derived using the forward algorithm. The generators of the mesonic moduli space are determined using Hilbert series. The spectrum of scaling dimensions for chiral operators is computed.Comment: 128 pages, 39 figures, 42 table

Neu3 Activity Enhances Egfr Activation Without Affecting Egfr Expression

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New results for the SQCD Hilbert series

We derive new explicit results for the Hilbert series of N=1 supersymmetric QCD with U(N_c) and SU(N_c) color symmetry. We use two methods which have previously been applied to similar computational problems in the analysis of decay of unstable D-branes: expansions using Schur polynomials, and the log-gas approach related to random matrix theory.Comment: 33 pages, 2 figures; v2: references and comments on the 3rd order phase transition added; v3: refs. correcte

Toric AdS4/CFT3 duals and M-theory Crystals

We study the recently proposed crystal model for three dimensional superconformal field theories arising from M2-branes probing toric Calabi-Yau four-fold singularities. We explain the algorithms mapping a toric Calabi-Yau to a crystal and vice versa, and show how the spectrum of BPS meson states fits into the crystal model.Comment: 24 pages, 24 figure