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

Lung volume reduction reoperations

BACKGROUND: Optimal management of emphysematous patients who have lost the benefits achieved after lung volume reduction surgery is a clinical dilemma. We have hypothesized that in stringently selected instances, lung volume reduction reoperations might be considered as a salvage surgical treatment. We sought to analyze the results of a series of patients undergoing lung volume reduction reoperations after successful bilateral lung volume reduction surgery. METHODS: Between January 2000 and April 2006, 17 patients (mean age, 66 +/- 3 years) with radiologic evidence of distinct regional lung hyperinflation underwent lung volume reduction reoperations. Surgical procedures entailed completion lobectomy in 7 patients, nonanatomic resection of lung target areas were performed in 5 patients under general anesthesia with one-lung ventilation, and awake lung plication was performed in 5 patients under sole epidural anesthesia. Follow-up at 6 and 12 months was complete in all survivors. RESULTS: Mean operative time was 100 +/- 12 minutes. Two patients (11.7%) died perioperatively of adult respiratory distress syndrome. Hospital stay was 9 +/- 2 days. Significant improvements occurred for up to 12 months in forced expiratory volume in 1 second (FEV(1); p < 0.001), forced vital capacity (p < 0.002), residual volume (p < 0.001), 6-minute walk test (p < 0.001), and modified Medical Research Council dyspnea index (p < 0.001). At 6-months, improvements in FEV(1) were greater than 200 mL in 11 patients and correlated with the postoperative reduction in residual volume (r = -0.62, p = 0.01); baseline residual volume was inversely correlated with the degree of improvement in the dyspnea index (r = -0.54, p = 0.03). CONCLUSIONS: Lung volume reduction reoperations can offer significant clinical improvement to stringently selected patients who have lost the clinical benefit achieved after lung volume reduction surgery

Crop Species Diversity Changes in the United States: 1978-2012

Citation: Aguilar, J., Gramig, G. G., Hendrickson, J. R., Archer, D. W., Forcella, F., & Liebig, M. A. (2015). Crop Species Diversity Changes in the United States: 1978-2012. Plos One, 10(8), 14. doi:10.1371/journal.pone.0136580Anecdotal accounts regarding reduced US cropping system diversity have raised concerns about negative impacts of increasingly homogeneous cropping systems. However, formal analyses to document such changes are lacking. Using US Agriculture Census data, which are collected every five years, we quantified crop species diversity from 1978 to 2012, for the contiguous US on a county level basis. We used Shannon diversity indices expressed as effective number of crop species (ENCS) to quantify crop diversity. We then evaluated changes in county-level crop diversity both nationally and for each of the eight Farm Resource Regions developed by the National Agriculture Statistics Service. During the 34 years we considered in our analyses, both national and regional ENCS changed. Nationally, crop diversity was lower in 2012 than in 1978. However, our analyses also revealed interesting trends between and within different Resource Regions. Overall, the Heartland Resource Region had the lowest crop diversity whereas the Fruitful Rim and Northern Crescent had the highest. In contrast to the other Resource Regions, the Mississippi Portal had significantly higher crop diversity in 2012 than in 1978. Also, within regions there were differences between counties in crop diversity. Spatial autocorrelation revealed clustering of low and high ENCS and this trend became stronger over time. These results show that, nationally counties have been clustering into areas of either low diversity or high diversity. Moreover, a significant trend of more counties shifting to lower rather than to higher crop diversity was detected. The clustering and shifting demonstrates a trend toward crop diversity loss and attendant homogenization of agricultural production systems, which could have far-reaching consequences for provision of ecosystem system services associated with agricultural systems as well as food system sustainability

Scattering Amplitudes and Toric Geometry

In this paper we provide a first attempt towards a toric geometric interpretation of scattering amplitudes. In recent investigations it has indeed been proposed that the all-loop integrand of planar N=4 SYM can be represented in terms of well defined finite objects called on-shell diagrams drawn on disks. Furthermore it has been shown that the physical information of on-shell diagrams is encoded in the geometry of auxiliary algebraic varieties called the totally non negative Grassmannians. In this new formulation the infinite dimensional symmetry of the theory is manifest and many results, that are quite tricky to obtain in terms of the standard Lagrangian formulation of the theory, are instead manifest. In this paper, elaborating on previous results, we provide another picture of the scattering amplitudes in terms of toric geometry. In particular we describe in detail the toric varieties associated to an on-shell diagram, how the singularities of the amplitudes are encoded in some subspaces of the toric variety, and how this picture maps onto the Grassmannian description. Eventually we discuss the action of cluster transformations on the toric varieties. The hope is to provide an alternative description of the scattering amplitudes that could contribute in the developing of this very interesting field of research.Comment: 58 pages, 25 figures, typos corrected, a reference added, to be published in JHE

Counting Exceptional Instantons

We show how to obtain the instanton partition function of N=2 SYM with exceptional gauge group EFG using blow-up recursion relations derived by Nakajima and Yoshioka. We compute the two instanton contribution and match it with the recent proposal for the superconformal index of rank 2 SCFTs with E6, E7 global symmetry.Comment: 16 pages, references adde

M5 spikes and operators in the HVZ membrane theory

In this note we study some aspects of the so-called dual ABJM theory introduced by Hanany, Vegh & Zaffaroni. We analyze the spectrum of chiral operators, and compare it with the spectrum of functions on the mesonic moduli space M=C^2\times C^2/Z_k, finding expected agreement for the coherent branch. A somewhat mysterious extra branch of dimension N^2 opens up at the orbifold fixed point. We also study BPS solutions which represent M2/M5 intersections. The mesonic moduli space suggests that there should be two versions of this spike: one where the M5 lives in the orbifolded C^2 and another where it lives in the unorbifolded one. While expectedly the first class turns out to be like the ABJM spike, the latter class looks like a collection of stacks of M5 branes with fuzzy S^3 profiles. This shows hints of the appearance of the global SO(4) at the non-abelian level which is otherwise not present in the bosonic potential. We also study the matching of SUGRA modes with operators in the coherent branch of the moduli space. As a byproduct, we present some formulae for the laplacian in conical CY_4 of the form C^n\times CY_{4-n}.Comment: 22 pages, 1 figure. Published version with corrected typos

The Hilbert Series of the One Instanton Moduli Space

The moduli space of k G-instantons on R^4 for a classical gauge group G is known to be given by the Higgs branch of a supersymmetric gauge theory that lives on Dp branes probing D(p + 4) branes in Type II theories. For p = 3, these (3 + 1) dimensional gauge theories have N = 2 supersymmetry and can be represented by quiver diagrams. The F and D term equations coincide with the ADHM construction. The Hilbert series of the moduli spaces of one instanton for classical gauge groups is easy to compute and turns out to take a particularly simple form which is previously unknown. This allows for a G invariant character expansion and hence easily generalisable for exceptional gauge groups, where an ADHM construction is not known. The conjectures for exceptional groups are further checked using some new techniques like sewing relations in Hilbert Series. This is applied to Argyres-Seiberg dualities.Comment: 43 pages, 22 figure

Neutrino Masses, Baryon Asymmetry, Dark Matter and the Moduli Problem : A Complete Framework

Recent developments in string theory have led to "realistic" string compactifications which lead to moduli stabilization while generating a hierarchy between the Electroweak and Planck scales at the same time. However, this seems to suggest a rethink of our standard notions of cosmological evolution after the end of inflation and before the beginning of BBN. We argue that within classes of realistic string compactifications, there generically exists a light modulus with a mass comparable to that of the gravitino which generates a large late-time entropy when it decays. Therefore, all known mechanisms of generating the baryon asymmetry of the Universe in the literature have to take this fact into account. In this work, we find that it is still possible to naturally generate the observed baryon asymmetry of the Universe as well as light left-handed neutrino masses from a period of Affleck-Dine(AD) leptogenesis shortly after the end of inflation, in classes of realistic string constructions with a minimal extension of the MSSM below the unification scale (consisting only of right-handed neutrinos) and satisfying certain microscopic criteria described in the text. The consequences are as follows. The lightest left-handed neutrino is required to be virtually massless. The moduli (gravitino) problem can be naturally solved in this framework both within gravity and gauge mediation. The observed upper bound on the relic abundance constrains the moduli-matter and moduli-gravitino couplings since the DM is produced non-thermally within this framework. Finally, although not a definite prediction, the framework naturally allows a light right-handed neutrino and sneutrinos around the electroweak scale which could have important implications for DM as well as the LHC.Comment: 41 pages, no figures, journal version adde

The Large N Limit of Toric Chern-Simons Matter Theories and Their Duals

We compute the large N limit of the localized three dimensional free energy of various field theories with known proposed AdS duals. We show that vector-like theories agree with the expected supergravity results, and with the conjectured F-theorem. We also check that the large N free energy is preserved by the three dimensional Seiberg duality for general classes of vector like theories. Then we analyze the behavior of the free energy of chiral-like theories by applying a new proposal. The proposal is based on the restoration of a discrete symmetry on the free energy before the extremization. We apply this procedure at strong coupling in some examples and we discuss the results. We conclude the paper by proposing an alternative geometrical expression for the free energy.Comment: 40 pages, 7 figures, using jheppub.sty, references adde