The Relationship between Bare and Renormalized Couplings in Scalar Electrodynamics

When using dimensional regularization, the bare couplings are expressed as a power series in (2 - n/2)^{-1} where n is the number of dimensions. It is shown how the renormalization group can be used to sum the leading pole, next to leading pole etc. contributions to these sums in scalar electrodynamics (or any theory with multiple couplings.)Comment: 6 page

Frobenius Splittings

We give a gentle introduction to Frobenius splittings. Then we recall a few results that have been obtained with the method.Comment: 21 pages, typos correcte

Towards Deconstruction of the Type D (2,0) Theory

We propose a four-dimensional supersymmetric theory that deconstructs, in a particular limit, the six-dimensional $(2,0)$ theory of type $D_k$. This 4d theory is defined by a necklace quiver with alternating gauge nodes $\mathrm{O}(2k)$ and $\mathrm{Sp}(k)$. We test this proposal by comparing the 6d half-BPS index to the Higgs branch Hilbert series of the 4d theory. In the process, we overcome several technical difficulties, such as Hilbert series calculations for non-complete intersections, and the choice of $\mathrm{O}$ versus $\mathrm{SO}$ gauge groups. Consistently, the result matches the Coulomb branch formula for the mirror theory upon reduction to 3d

The ATF6-Met [67] Val substitution is associated with increased plasma cholesterol levels

Objective— Activating transcription factor 6 (ATF6) is a sensor of the endoplasmic reticulum stress response and regulates expression of several key lipogenic genes. We used a 2-stage design to investigate whether ATF6 polymorphisms are associated with lipids in subjects at increased risk for cardiovascular disease (CVD). Methods and Results— In stage 1, 13 tag-SNPs were tested for association in Dutch samples ascertained for familial combined hyperlipidemia (FCHL) or increased risk for CVD (CVR). In stage 2, we further investigated the SNP with the strongest association from stage 1, a Methionine/Valine substitution at amino-acid 67, in Finnish FCHL families and in subjects with CVR from METSIM, a Finnish population-based cohort. The combined analysis of both stages reached region-wide significance (P=9x10–4), but this association was not seen in the entire METSIM cohort. Our functional analysis demonstrated that Valine at position 67 augments ATF6 protein and its targets Grp78 and Grp94 as well as increases luciferase expression through Grp78 promoter. Conclusions— A common nonsynonymous variant in ATF6 increases ATF6 protein levels and is associated with cholesterol levels in subjects at increased risk for CVD, but this association was not seen in a population-based cohort. Further replication is needed to confirm the role of this variant in lipids. We report the association of the ATF6-methionine [67]valine amino-acid substitution with plasma cholesterol levels. Association analyses in 2674 subjects and functional data suggest that the ATF6 gene may influence cholesterol levels in subjects at increased risk to develop cardiovascular disease

M5-branes from gauge theories on the 5-sphere

We use the 5-sphere partition functions of supersymmetric Yang-Mills theories to explore the (2,0) superconformal theory on S^5 x S^1. The 5d theories can be regarded as Scherk-Schwarz reductions of the 6d theory along the circle. In a special limit, the perturbative partition function takes the form of the Chern-Simons partition function on S^3. With a simple non-perturbative completion, it becomes a 6d index which captures the degeneracy of a sector of BPS states as well as the index version of the vacuum Casimir energy. The Casimir energy exhibits the N^3 scaling at large N. The large N index for U(N) gauge group also completely agrees with the supergravity index on AdS_7 x S^4.Comment: 44 pages, 1 figure, v4: ref added, clarified weak/strong coupling behaviors of large N free energy, minor improvements, version to be published in JHE

Exploring Curved Superspace

We systematically analyze Riemannian manifolds M that admit rigid supersymmetry, focusing on four-dimensional N=1 theories with a U(1)_R symmetry. We find that M admits a single supercharge, if and only if it is a Hermitian manifold. The supercharge transforms as a scalar on M. We then consider the restrictions imposed by the presence of additional supercharges. Two supercharges of opposite R-charge exist on certain fibrations of a two-torus over a Riemann surface. Upon dimensional reduction, these give rise to an interesting class of supersymmetric geometries in three dimensions. We further show that compact manifolds admitting two supercharges of equal R-charge must be hyperhermitian. Finally, four supercharges imply that M is locally isometric to M_3 x R, where M_3 is a maximally symmetric space.Comment: 39 pages; minor change

Quantum Electrodynamics of the Helium Atom

Using singlet S states of the helium atom as an example, I describe precise calculation of energy levels in few-electron atoms. In particular, a complete set of effective operators is derived which generates O(m*alpha^6) relativistic and radiative corrections to the Schr"odinger energy. Average values of these operators can be calculated using a variational Schr"odinger wave function.Comment: 23 pages, revte

The compositional and evolutionary logic of metabolism

Metabolism displays striking and robust regularities in the forms of modularity and hierarchy, whose composition may be compactly described. This renders metabolic architecture comprehensible as a system, and suggests the order in which layers of that system emerged. Metabolism also serves as the foundation in other hierarchies, at least up to cellular integration including bioenergetics and molecular replication, and trophic ecology. The recapitulation of patterns first seen in metabolism, in these higher levels, suggests metabolism as a source of causation or constraint on many forms of organization in the biosphere. We identify as modules widely reused subsets of chemicals, reactions, or functions, each with a conserved internal structure. At the small molecule substrate level, module boundaries are generally associated with the most complex reaction mechanisms and the most conserved enzymes. Cofactors form a structurally and functionally distinctive control layer over the small-molecule substrate. Complex cofactors are often used at module boundaries of the substrate level, while simpler ones participate in widely used reactions. Cofactor functions thus act as "keys" that incorporate classes of organic reactions within biochemistry. The same modules that organize the compositional diversity of metabolism are argued to have governed long-term evolution. Early evolution of core metabolism, especially carbon-fixation, appears to have required few innovations among a small number of conserved modules, to produce adaptations to simple biogeochemical changes of environment. We demonstrate these features of metabolism at several levels of hierarchy, beginning with the small-molecule substrate and network architecture, continuing with cofactors and key conserved reactions, and culminating in the aggregation of multiple diverse physical and biochemical processes in cells.Comment: 56 pages, 28 figure

A 5d/3d duality from relativistic integrable system

We propose and prove a new exact duality between the F-terms of supersymmetric gauge theories in five and three dimensions with adjoint matter fields. The theories are compactified on a circle and are subject to the Omega deformation. In the limit proposed by Nekrasov and Shatashvili, the supersymmetric vacua become isolated and are identified with the eigenstates of a quantum integrable system. The effective twisted superpotentials are the Yang-Yang functional of the relativistic elliptic Calogero-Moser model. We show that they match on-shell by deriving the Bethe ansatz equation from the saddle point of the five-dimensional partition function. We also show that the Chern-Simons terms match and extend our proposal to the elliptic quiver generalizations.Comment: 30 pages, 4 figures. v2: typo corrected, references adde

Learning through social spaces: migrant women and lifelong learning in post-colonial London

This article shows how migrant women engage in learning through social spaces. It argues that such spaces are little recognised, and that there are multiple ways in which migrant women construct and negotiate their informal learning through socialising with other women in different informal modes. Additionally, the article shows how learning is shaped by the socio-political, geographical and multicultural context of living in London, outlining ways in which gendered and racialised identities shape, construct and constrain participation in lifelong learning. The article shows that one way in which migrant women resist (post)colonial constructions of difference is by engaging in informal and non-formal lifelong learning, arguing that the benefits are (at least) two-fold. The women develop skills (including language skills) but also use their informal learning to develop what is referred to in this article as 'relational capital'. The article concludes that informal lifelong learning developed through social spaces can enhance a sense of belonging for migrant women