The Soft-Collinear Bootstrap: N=4 Yang-Mills Amplitudes at Six and Seven Loops

Infrared divergences in scattering amplitudes arise when a loop momentum $\ell$ becomes collinear with a massless external momentum $p$. In gauge theories, it is known that the L-loop logarithm of a planar amplitude has much softer infrared singularities than the L-loop amplitude itself. We argue that planar amplitudes in N=4 super-Yang-Mills theory enjoy softer than expected behavior as $\ell \parallel p$ already at the level of the integrand. Moreover, we conjecture that the four-point integrand can be uniquely determined, to any loop-order, by imposing the correct soft-behavior of the logarithm together with dual conformal invariance and dihedral symmetry. We use these simple criteria to determine explicit formulae for the four-point integrand through seven-loops, finding perfect agreement with previously known results through five-loops. As an input to this calculation we enumerate all four-point dual conformally invariant (DCI) integrands through seven-loops, an analysis which is aided by several graph-theoretic theorems we prove about general DCI integrands at arbitrary loop-order. The six- and seven-loop amplitudes receive non-zero contributions from 229 and 1873 individual DCI diagrams respectively.Comment: 27 pages, 48 figures, detailed results including PDF and Mathematica files available at http://goo.gl/qIKe8 v2: minor corrections v3: figure 7 corrected, Lemma 2 remove

Five-loop renormalisation of QCD in covariant gauges

We present the complete set of vertex, wave function and charge renormalisation constants in QCD in a general simple gauge group and with the complete dependence on the covariant gauge parameter $\xi$ in the minimal subtraction scheme of conventional dimensional regularisation. Our results confirm all already known results, which were obtained in the Feynman gauge, and allow the extraction of other useful gauges such as the Landau gauge. We use these results to extract the Landau gauge five-loop anomalous dimensions of the composite operator $A^2$ as well as the Landau gauge scheme independent gluon, ghost and fermion propagators at five loops.Comment: 17 pages; FORM and Mathematica result files available with the source; corrected minor typos, added references, journal ref, 1 remark, 1 note and 1 additional result fil

Agronomic Management of Indigenous Mycorrhizas

Many of the advantages conferred to plants by arbuscular mycorrhiza (AM) are associated to the ability of AM plants to explore a greater volume of soil through the extraradical mycelium. Sieverding (1991) estimates that for each centimetre of colonized root there is an increase of 15 cm3 on the volume of soil explored, this value can increase to 200 cm3 depending on the circumstances. Due to the enhancement of the volume of soil explored and the ability of the extraradical mycelium to absorb and translocate nutrients to the plant, one of the most obvious and important advantages resulting from mycorrhization is the uptake of nutrients. Among of which the ones that have immobilized forms in soil, such as P, assume particular significance. Besides this, many other benefits are recognized for AM plants (Gupta et al, 2000): water stress alleviation (Augé, 2004; Cho et al, 2006), protection from root pathogens (Graham, 2001), tolerance to toxic heavy metals and phytoremediation (Audet and Charest, 2006; Göhre and Paszkowski, 2006), tolerance to adverse conditions such as very high or low temperature, high salinity (Sannazzaro et al, 2006), high or low pH (Yano and Takaki, 2005) or better performance during transplantation shock (Subhan et al, 1998). The extraradical hyphae also stabilize soil aggregates by both enmeshing soil particles (Miller e Jastrow, 1992) and producing a glycoprotein, golmalin, which may act as a glue-like substance to adhere soil particles together (Wright and Upadhyaya, 1998). Despite the ubiquous distribution of mycorrhizal fungi (Smith and Read, 2000) and only a relative specificity between host plants and fungal isolates (McGonigle and Fitter, 1990), the obligate nature of the symbiosis implies the establishment of a plant propagation system, either under greenhouse conditions or in vitro laboratory propagation. These techniques result in high inoculum production costs, which still remains a serious problem since they are not competitive with production costs of phosphorus fertilizer. Even if farmers understand the significance of sustainable agricultural systems, the reduction of phosphorus inputs by using AM fungal inocula alone cannot be justified except, perhaps, in the case of high value crops (Saioto and Marumoto, 2002). Nurseries, high income horticulture farmers and no-agricultural application such as rehabilitation of degraded or devegetated landscapes are examples of areas where the use of commercial inoculum is current. Another serious problem is quality of commercial available products concerning guarantee of phatogene free content, storage conditions, most effective application methods and what types to use. Besides the information provided by suppliers about its inoculum can be deceiving, as from the usually referred total counts, only a fraction may be effective for a particular plant or in specific soil conditions. Gianinazzi and Vosátka (2004) assume that progress should be made towards registration procedures that stimulate the development of the mycorrhizal industry. Some on-farm inoculum production and application methods have been studied, allowing farmers to produce locally adapted isolates and generate a taxonomically diverse inoculum (Mohandas et al, 2004; Douds et al, 2005). However the inocula produced this way are not readily processed for mechanical application to the fields, being an obstacle to the utilization in large scale agriculture, especially row crops, moreover it would represent an additional mechanical operation with the corresponding economic and soil compaction costs. It is well recognized that inoculation of AM fungi has a potential significance in not only sustainable crop production, but also environmental conservation. However, the status quo of inoculation is far from practical technology that can be widely used in the field. Together a further basic understanding of the biology and diversity of AM fungi is needed (Abbott at al, 1995; Saito and Marumoto, 2002). Advances in ecology during the past decade have led to a much more detailed understanding of the potential negative consequences of species introductions and the potential for negative ecological consequences of invasions by mycorrhizal fungi is poorly understood. Schwartz et al, (2006) recommend that a careful assessment documenting the need for inoculation, and the likelihood of success, should be conducted prior to inoculation because inoculations are not universally beneficial. Agricultural practices such as crop rotation, tillage, weed control and fertilizer apllication all produce changes in the chemical, physical and biological soil variables and affect the ecological niches available for occupancy by the soil biota, influencing in different ways the symbiosis performance and consequently the inoculum development, shaping changes and upset balance of native populations. The molecular biology tools developed in the latest years have been very important for our perception of these changes, ensuing awareness of management choice implications in AM development. In this context, for extensive farming systems and regarding environmental and economic costs, the identification of agronomic management practices that allow controlled manipulation of the fungal community and capitalization of AM mutualistic effect making use of local inoculum, seem to be a wise option for mycorrhiza promotion and development of sustainable crop production

What traits are carried on mobile genetic elements, and why?

Although similar to any other organism, prokaryotes can transfer genes vertically from mother cell to daughter cell, they can also exchange certain genes horizontally. Genes can move within and between genomes at fast rates because of mobile genetic elements (MGEs). Although mobile elements are fundamentally self-interested entities, and thus replicate for their own gain, they frequently carry genes beneficial for their hosts and/or the neighbours of their hosts. Many genes that are carried by mobile elements code for traits that are expressed outside of the cell. Such traits are involved in bacterial sociality, such as the production of public goods, which benefit a cell's neighbours, or the production of bacteriocins, which harm a cell's neighbours. In this study we review the patterns that are emerging in the types of genes carried by mobile elements, and discuss the evolutionary and ecological conditions under which mobile elements evolve to carry their peculiar mix of parasitic, beneficial and cooperative genes