Selfdual strings and loop space Nahm equations

We give two independent arguments why the classical membrane fields should be loops. The first argument comes from how we may construct selfdual strings in the M5 brane from a loop space version of the Nahm equations. The second argument is that there appears to be no infinite set of finite-dimensional Lie algebras (such as $su(N)$ for any $N$) that satisfies the algebraic structure of the membrane theory.Comment: 28 pages, various additional comment

PhytoMilk

Potential improvement of the salutary effect of organic dairy milk by forage species and by supplementation

Loop space, (2,0) theory, and solitonic strings

We present an interacting action that lives in loop space, and we argue that this is a generalization of the theory for a free tensor multiplet. From this action we derive the Bogomolnyi equation corresponding to solitonic strings. Using the Hopf map, we find a correspondence between BPS strings and BPS monopoles in four-dimensional super Yang-Mills theory. This enable us to find explicit BPS saturated solitonic string solutions.Comment: 29 pages, v3: section 5 is rewritten and string solutions are found, v4: a new section on general covariance in loop spac

Superalgebra Realization of the 3-algebras in N=6, 8 Chern-Simons-matter Theories

We use superalgebras to realize the 3-algebras used to construct N=6, 8 Chern-Simons-matter (CSM) theories. We demonstrate that the superalgebra realization of the 3-algebras provides a unified framework for classifying the gauge groups of the N \geq 5 theories based on 3-algebras. Using this realization, we rederive the ordinary Lie algebra construction of the general N=6 CSM theory from its 3-algebra counterpart, and reproduce all known examples as well. In particular, we explicitly construct the Nambu 3-bracket in terms of a double graded commutator of PSU(2|2). The N = 8 theory of Bagger, Lambert and Gustavsson (BLG) with SO(4) gauge group is constructed by using several different ways. A quantization scheme for the 3-brackets is proposed by promoting the double graded commutators as quantum mechanical double graded commutators.Comment: 29 pages, minor changes, published in JM

Initial soil structural development under different types of vegetation

In September 2007, undisturbed soil cores were taken from experimental fields in The Netherlands and in Northern Sweden that had been under different types of vegetation during four years. From these cores, thin sections were prepared to study the initial soil structural development, changes in organic matter distribution and soil biological activity in relation to plant species growing on the plots. In the Swedish samples, differences between plots with Poa pratensis and Phleum pratense were striking. The Poa plot showed more filled biological burrows, more rounded soil aggregates and also the amount of fine disperse organic matter seemed higher, whereas under Phleum the individual mineral grains more often showed a thin coating of very fine organic matter. Plots with Trifolium repens showed a slightly less pronounced development when compared to the Poa plots. The plots of Trifolium pratense plots and the mixed plot showed highest amounts of biological activity and soil structural development. The samples taken from the clay soils from The Netherlands showed similar biological activity under pure Lolium perenne and binary mixtures of L. perenne with the legumes T. repens, T. pratense and Medicago sativa from a trial that was not fertilized with N. A high activity of Lumbricus festi was shown by common excremental pellets in channels. In contrast, under Achillea millefolium in an adjacent N fertilised experiment, this activity was completely absent

Thomson scattering of chiral tensors and scalars against a self-dual string

We give a non-technical outline of a program to study the (2,0) theories in six space-time dimensions. Away from the origin of their moduli space, these theories describe the interactions of tensor multiplets and self-dual spinning strings. We argue that if the ratio between the square of the energy of a process and the string tension is taken to be small, it should be possible to study the dynamics of such a system perturbatively in this parameter. As a first step in this direction, we perform a classical computation of the amplitude for scattering chiral tensor and scalar fields (i.e. the bosonic part of a tensor multiplet) against a self-dual spinnless string.Comment: 24 pages, LaTeX, 2 figures. v2: added discussion on supersymmetry in Ch.

The non-Abelian tensor multiplet in loop space

We introduce a non-Abelian tensor multiplet directly in the loop space associated with flat six-dimensional Minkowski space-time, and derive the supersymmetry variations for on-shell ${\cal{N}}=(2,0)$ supersymmetry.Comment: 11 pages, v2: cleaner presentation, mistakes are corrected (and an erroneous section was removed

Five-dimensional SYM from undeformed ABJM

We expand undeformed ABJM theory around the vacuum solution that was found in arxiv:0909.3101. This solution can be interpreted as a circle-bundle over a two-dimensional plane with a singularity at the origin. By imposing periodic boundary conditions locally far away from the singularity, we obtain a local fuzzy two-torus over which we have a circle fibration. By performing fluctuation analysis we obtain five-dimensional SYM with the precise value on the coupling constant that we would obtain by compactifying multiple M5 branes on the vacuum three-manifold. In the resulting SYM theory we also find a coupling to a background two-form.Comment: 23 page

Classical self-dual strings in d=6, (2,0) theory from afar

We show how one can get solitonic strings in a six-dimensional (2,0) supersymmetric theory by incorporating a nonlinear interaction term. We derive a zero force condition between parallel strings, and compute a metric on a moduli space which is $R^4$ when the strings are far apart. When compactifying the strings on a two-torus we show that, in the limit of vanishing two-torus, one regains the moduli space of two widely separated dyons of equal magnetic charges in four dimensions.Comment: 13 pages, clarifications and added reference

Conformal anomaly of Wilson surface observables - a field theoretical computation

We make an exact field theoretical computation of the conformal anomaly for two-dimensional submanifold observables. By including a scalar field in the definition for the Wilson surface, as appropriate for a spontaneously broken A_1 theory, we get a conformal anomaly which is such that N times it is equal to the anomaly that was computed in hep-th/9901021 in the large N limit and which relied on the AdS-CFT correspondence. We also show how the spherical surface observable can be expressed as a conformal anomaly.Comment: 18 pages, V3: an `i' dropped in the Wilson surface, overall normalization and misprints corrected, V4: overall normalization factor corrected, references adde