A community-driven paired data platform to accelerate natural product mining by combining structural information from genomes and metabolomes

Natural products are small molecules produced by bacteria, fungi, and plants that have a large variety of functions, including chemical defence and communication. Moreover, many of those natural products are exploited for therapeutic or medicinal use. For example, many antibiotics have natural products as origin ..

A locally finite model for gravity

Matter interacting classically with gravity in 3+1 dimensions usually gives rise to a continuum of degrees of freedom, so that, in any attempt to quantize the theory, ultraviolet divergences are nearly inevitable. Here, we investigate matter of a form that only displays a finite number of degrees of freedom in compact sections of space-time. In finite domains, one has only exact, analytic solutions. This is achieved by limiting ourselves to straight pieces of string, surrounded by locally flat sections of space-time. Globally, however, the model is not finite, because solutions tend to generate infinite fractals. The model is not (yet) quantized, but could serve as an interesting setting for analytical approaches to classical general relativity, as well as a possible stepping stone for quantum models. Details of its properties are explained, but some problems remain unsolved, such as a complete description of the most violent interactions, which can become quite complex.Comment: 26 pages, 9 figure

Simplifications of four-point functions in N=4 supersymmetric Yang-Mills theory at two loops

The superconformal Ward identities combined with N=2 harmonic analyticity are used to evaluate two-loop four-point correlation functions of gauge-invariant operators in D=4, N=4 supersymmetric Yang-Mills theory in terms of the well-known one-loop box integral. The result is confirmed by a direct numerical computation

Low-energy spectrum of N = 4 super-Yang-Mills on T^3: flat connections, bound states at threshold, and S-duality

We study (3+1)-dimensional N=4 supersymmetric Yang-Mills theory on a spatial three-torus. The low energy spectrum consists of a number of continua of states of arbitrarily low energies. Although the theory has no mass-gap, it appears that the dimensions and discrete abelian magnetic and electric 't Hooft fluxes of the continua are computable in a semi-classical approximation. The wave-functions of the low-energy states are supported on submanifolds of the moduli space of flat connections, at which various subgroups of the gauge group are left unbroken. The field theory degrees of freedom transverse to such a submanifold are approximated by supersymmetric matrix quantum mechanics with 16 supercharges, based on the semi-simple part of this unbroken group. Conjectures about the number of normalizable bound states at threshold in the latter theory play a crucial role in our analysis. In this way, we compute the low-energy spectra in the cases where the simply connected cover of the gauge group is given by SU(n), Spin(2n+1) or Sp(2n). We then show that the constraints of S-duality are obeyed for unique values of the number of bound states in the matrix quantum mechanics. In the cases based on Spin(2n+1) and Sp(2n), the proof involves surprisingly subtle combinatorial identities, which hint at a rich underlying structure.Comment: 28 pages. v2:reference adde

Explicit construction of nilpotent covariants in N=4 SYM

Some aspects of correlation functions in N=4 SYM are discussed. Using N=4 harmonic superspace we study two and three-point correlation functions which are of contact type and argue that these contact terms will not affect the non-renormalisation theorem for such correlators at non-coincident points. We then present a perturbative calculation of a five-point function at two loops in N=2 harmonic superspace and verify that it reproduces the derivative of the previously found four-point function with respect to the coupling. The calculation of this four-point function via the five-point function turns out to be significantly simpler than the original direct calculation. This calculation also provides an explicit construction of an N=2 component of an N=4 five-point nilpotent covariant that violates U(1)_Y symmetry.Comment: 20 pages, standard late

Interaction of global and local monopoles

We study the direct interaction between global and local monopoles. While in two previous papers, the coupling between the two sectors was only indirect through the coupling to gravity, we here introduce a new term in the potential that couples the Goldstone field and the Higgs field directly. We investigate the influence of this term in curved space and compare it to the results obtained previously.Comment: 9 Revtex pages, 4 ps-figure

Matrix Models, Argyres-Douglas singularities and double scaling limits

We construct an N=1 theory with gauge group U(nN) and degree n+1 tree level superpotential whose matrix model spectral curve develops an A_{n+1} Argyres-Douglas singularity. We evaluate the coupling constants of the low-energy U(1)^n theory and show that the large N expansion is singular at the Argyres-Douglas points. Nevertheless, it is possible to define appropriate double scaling limits which are conjectured to yield four dimensional non-critical string theories as proposed by Ferrari. In the Argyres-Douglas limit the n-cut spectral curve degenerates into a solution with n/2 cuts for even n and (n+1)/2 cuts for odd n.Comment: 31 pages, 1 figure; the expression of the superpotential has been corrected and the calculation of the coupling constants of the low-energy theory has been adde

SS-duality in Vafa-Witten theory for non-simply laced gauge groups

Vafa-Witten theory is a twisted N=4 supersymmetric gauge theory whose partition functions are the generating functions of the Euler number of instanton moduli spaces. In this paper, we recall quantum gauge theory with discrete electric and magnetic fluxes and review the main results of Vafa-Witten theory when the gauge group is simply laced. Based on the transformations of theta functions and their appearance in the blow-up formulae, we propose explicit transformations of the partition functions under the Hecke group when the gauge group is non-simply laced. We provide various evidences and consistency checks.Comment: 14 page

Anisotropic scale invariant cosmology

We study a possibility of anisotropic scale invariant cosmology. It is shown that within the conventional Einstein gravity, the violation of the null energy condition is necessary. We construct an example based on a ghost condensation model that violates the null energy condition. The cosmological solution necessarily contains at least one contracting spatial direction as in the Kasner solution. Our cosmology is conjectured to be dual to, if any, a non-unitary anisotropic scale invariant Euclidean field theory. We investigate simple correlation functions of the dual theory by using the holographic computation. After compactification of the contracting direction, our setup may yield a dual field theory description of the winding tachyon condensation that might solve the singularity of big bang/crunch of the universe.Comment: 12 pages, v2: reference adde

Dyonic Non-Abelian Black Holes

We study static spherically symmetric dyonic black holes in Einstein-Yang-Mills-Higgs theory. As for the magnetic non-abelian black holes, the domain of existence of the dyonic non-abelian black holes is limited with respect to the horizon radius and the dimensionless coupling constant $\alpha$, which is proportional to the ratio of vector meson mass and Planck mass. At a certain critical value of this coupling constant, $\hat \alpha$, the maximal horizon radius is attained. We derive analytically a relation between $\hat \alpha$ and the charge of the black hole solutions and confirm this relation numerically. Besides the fundamental dyonic non-abelian black holes, we study radially excited dyonic non-abelian black holes and globally regular gravitating dyons.Comment: LaTeX, 22 pages, 16 figures, three figures added, file manipulation error in previous replac