Stringy Instantons in SU(N) N=2 Non-Conformal Gauge Theories

In this paper we explicitly obtain the leading corrections to the SU(N) N=2 prepotential due to stringy instantons both in flat space-time and in the presence of a non-trivial graviphoton background field. We show that the stringy corrections to the prepotential are expressible in terms of the elementary symmetric polynomials. For N>2 the theory is not conformal; we discuss the introduction of an explicit dependence on the string scale \alpha' in the low-energy effective action through the stringy non-perturbative sector.Comment: 22 pages, 1 figur

Holographic non-perturbative corrections to gauge couplings

We give a direct microscopic derivation of the F-theory background that corresponds to four D7 branes of type I' theory by taking into account the D-instanton contributions to the emission of the axio-dilaton field in the directions transverse to the D7's. The couplings of the axio-dilaton to the D-instanton moduli modify its classical source terms which are shown to be proportional to the elements of the D7 brane chiral ring. Solving the bulk field equations with the non-perturbatively corrected sources yields the full F-theory background. This solution represents the gravitational dual of the four-dimensional theory living on a probe D3 brane of type I', namely of the N=2, Sp(1) SYM theory with Nf=4. Our results provide an explicit microscopic derivation of the non-perturbative gravitational dual of this theory. They also explain the recent observation that the exact coupling for this theory can be entirely reconstructed from its perturbative part plus the knowledge of the chiral ring on the D7 branes supporting its flavor degrees of freedom.Comment: Latex, 39 pages, 6 figure

Stringy instanton corrections to N=2 gauge couplings

We discuss a string model where a conformal four-dimensional N=2 gauge theory receives corrections to its gauge kinetic functions from "stringy" instantons. These contributions are explicitly evaluated by exploiting the localization properties of the integral over the stringy instanton moduli space. The model we consider corresponds to a setup with D7/D3-branes in type I' theory compactified on T4/Z2 x T2, and possesses a perturbatively computable heterotic dual. In the heteoric side the corrections to the quadratic gauge couplings are provided by a 1-loop threshold computation and, under the duality map, match precisely the first few stringy instanton effects in the type I' setup. This agreement represents a very non-trivial test of our approach to the exotic instanton calculus.Comment: 63 pages, 5 figures. V2: final version with minor corrections published on JHEP05(2010)10

A Survey on Continuous Time Computations

We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models. We survey the existing models, summarizing results, and point to relevant references in the literature

On-shell Recursion in String Theory

We prove that all open string theory disc amplitudes in a flat background obey Britto-Cachazo-Feng-Witten (BCFW) on-shell recursion relations, up to a possible reality condition on a kinematic invariant. Arguments that the same holds for tree level closed string amplitudes are given as well. Non-adjacent BCFW-shifts are related to adjacent shifts through monodromy relations for which we provide a novel CFT based derivation. All possible recursion relations are related by old-fashioned string duality. The field theory limit of the analysis for amplitudes involving gluons is explicitly shown to be smooth for both the bosonic string as well as the superstring. In addition to a proof a less rigorous but more powerful argument based on the underlying CFT is presented which suggests that the technique may extend to a much more general setting in string theory. This is illustrated by a discussion of the open string in a constant B-field background and the closed string on the level of the sphere.Comment: 36 + 9 pages text, one figure, v3: added discussion on relation to old-fashioned factorization, typos corrected, published versio

Static Charges in the Low-Energy Theory of the S-Duality Twist

We continue the study of the low-energy limit of N=4 super Yang-Mills theory compactified on a circle with S-duality and R-symmetry twists that preserve N=6 supersymmetry in 2+1D. We introduce external static supersymmetric quark and anti-quark sources into the theory and calculate the Witten Index of the resulting Hilbert space of ground states on a torus. Using these results we compute the action of simple Wilson loops on the Hilbert space of ground states without sources. In some cases we find disagreement between our results for the Wilson loop eigenvalues and previous conjectures about a connection with Chern-Simons theory.Comment: 73 pages, two paragraphs added, one to the introduction and one to the discussio

GLSMs for non-Kahler Geometries

We identify a simple mechanism by which H-flux satisfying the modified Bianchi identity arises in garden-variety (0,2) gauged linear sigma models. Taking suitable limits leads to effective gauged linear sigma models with Green-Schwarz anomaly cancellation. We test the quantum-consistency of a class of such effective theories by constructing an off-shell superconformal algebra, providing evidence that these models run to good CFTs in the deep IR.Comment: 37 pages, Minor updates for v

Charge Lattices and Consistency of 6D Supergravity

We extend the known consistency conditions on the low-energy theory of six-dimensional N = 1 supergravity. We review some facts about the theory of two-form gauge fields and conclude that the charge lattice Gamma for such a theory has to be self-dual. The Green-Schwarz anomaly cancellation conditions in the supergravity theory determine a sublattice of Gamma. The condition that this sublattice can be extended to a self-dual lattice Gamma leads to a strong constraint on theories that otherwise appear to be self-consistent.Comment: 15 pages. v2: minor changes; references, additional example added; v3: minor corrections and clarifications added, JHEP versio

Non-perturbative gauge/gravity correspondence in N=2 theories

We derive the exact supergravity profile for the twisted scalar field emitted by a system of fractional D3 branes at a Z2 orbifold singularity supporting N=2 quiver gauge theories with unitary groups and bifundamental matter. At the perturbative level this twisted field is "dual" to the gauge coupling but it is corrected non-perturbatively by an infinite tower of fractional D-instantons. The explicit microscopic description allows to derive the gravity profile from disk amplitudes computing the emission rate of the twisted scalar field in terms of chiral correlators in the dual gauge theory. We compute these quantum correlators using multi-instanton localization techniques and/or Seiberg-Witten analysis. Finally, we discuss a non-perturbative relation between the twisted scalar and the effective coupling of the gauge theory for some simple choices of the brane set ups.Comment: 42 pages. 3 figures, PDFLaTe

Effect of four plant species on soil 15N-access and herbage yield in temporary agricultural grasslands

Positive plant diversity-productivity relationships have been reported for experimental semi-natural grasslands (Cardinale et al. 2006; Hector et al. 1999; Tilman et al. 1996) as well as temporary agricultural grasslands (Frankow-Lindberg et al. 2009; Kirwan et al. 2007; Nyfeler et al. 2009; Picasso et al. 2008). Generally, these relationships are explained, on the one hand, by niche differentiation and facilitation (Hector et al. 2002; Tilman et al. 2002) and, on the other hand, by greater probability of including a highly productive plant species in high diversity plots (Huston 1997). Both explanations accept that diversity is significant because species differ in characteristics, such as root architecture, nutrient acquisition and water use efficiency, to name a few, resulting in composition and diversity being important for improved productivity and resource use (Naeem et al. 1994; Tilman et al. 2002). Plant diversity is generally low in temporary agricultural grasslands grown for ruminant fodder production. Grass in pure stands is common, but requires high nitrogen (N) inputs. In terms of N input, two-species grass-legume mixtures are more sustainable than grass in pure stands and consequently dominate low N input grasslands (Crews and Peoples 2004; Nyfeler et al. 2009; Nyfeler et al. 2011). In temperate grasslands, N is often the limiting factor for productivity (Whitehead 1995). Plant available soil N is generally concentrated in the upper soil layers, but may leach to deeper layers, especially in grasslands that include legumes (Scherer-Lorenzen et al. 2003) and under conditions with surplus precipitation (Thorup-Kristensen 2006). To improve soil N use efficiency in temporary grasslands, we propose the addition of deep-rooting plant species to a mixture of perennial ryegrass and white clover, which are the most widespread forage plant species in temporary grasslands in a temperate climate (Moore 2003). Perennial ryegrass and white clover possess relatively shallow root systems (Kutschera and Lichtenegger 1982; Kutschera and Lichtenegger 1992) with effective rooting depths of <0.7 m on a silt loamy site (Pollock and Mead 2008). Grassland species, such as lucerne and chicory, grow their tap-roots into deep soil layers and exploit soil nutrients and water in soil layers that the commonly grown shallow-rooting grassland species cannot reach (Braun et al. 2010; Skinner 2008). Chicory grown as a catch crop after barley reduced the inorganic soil N down to 2.5 m depth during the growing season, while perennial ryegrass affected the inorganic soil N only down to 1 m depth (Thorup-Kristensen 2006). Further, on a Wakanui silt loam in New Zealand chicory extracted water down to 1.9 m and lucerne down to 2.3 m soil depth, which resulted in greater herbage yields compared with a perennial ryegrass-white clover mixture, especially for dryland plots (Brown et al. 2005). There is little information on both the ability of deep- and shallow-rooting grassland species to access soil N from different vertical soil layers and the relation of soil N-access and herbage yield in temporary agricultural grasslands. Therefore, the objective of the present work was to test the hypotheses 1) that a mixture comprising both shallow- and deep-rooting plant species has greater herbage yields than a shallow-rooting binary mixture and pure stands, 2) that deep-rooting plant species (chicory and lucerne) are superior in accessing soil N from 1.2 m soil depth compared with shallow-rooting plant species, 3) that shallow-rooting plant species (perennial ryegrass and white clover) are superior in accessing soil N from 0.4 m soil depth compared with deep-rooting plant species, 4) that a mixture of deep- and shallow-rooting plant species has greater access to soil N from three soil layers compared with a shallow-rooting two-species mixture and that 5) the leguminous grassland plants, lucerne and white clover, have a strong impact on grassland N acquisition, because of their ability to derive N from the soil and the atmosphere