Finite Schur filtration dimension for modules over an algebra with Schur filtration

Let G be GL_N or SL_N as reductive linear algebraic group over a field k of positive characteristic p. We prove several results that were previously established only when N 2^N. Let G act rationally on a finitely generated commutative k-algebra A. Assume that A as a G-module has a good filtration or a Schur filtration. Let M be a noetherian A-module with compatible G action. Then M has finite good/Schur filtration dimension, so that there are at most finitely many nonzero H^i(G,M). Moreover these H^i(G,M) are noetherian modules over the ring of invariants A^G. Our main tool is a resolution involving Schur functors of the ideal of the diagonal in a product of Grassmannians.Comment: 22 pages; final versio

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

Producing valid statistics when legislation, culture, and medical practices differ for births at or before the threshold of survival: Report of a European workshop

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Two-Loop Polarization Contributions to Radiative-Recoil Corrections to Hyperfine Splitting in Muonium

We calculate radiative-recoil corrections of order $\alpha^2(Z\alpha)(m/M)E_F$ to hyperfine splitting in muonium generated by the diagrams with electron and muon polarization loops. These corrections are enhanced by the large logarithm of the electron-muon mass ratio. The leading logarithm cubed and logarithm squared contributions were obtained a long time ago. The single-logarithmic and nonlogarithmic contributions calculated here improve the theory of hyperfine splitting, and affect the value of the electron-muon mass ratio extracted from the experimental data on the muonium hyperfine splitting.Comment: 15 pages, 11 figure

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

5-dim Superconformal Index with Enhanced En Global Symmetry

The five-dimensional $\mathcal{N}=1$ supersymmetric gauge theory with Sp(N) gauge group and SO(2N_f) flavor symmetry describes the physics on N D4-branes with $N_f$ D8-branes on top of a single O8 orientifold plane in Type I' theory. This theory is known to be superconformal at the strong coupling limit with the enhanced global symmetry $E_{N_f+1}$ for $N_f\le 7$. In this work we calculate the superconformal index on $S^1\times S^4$ for the Sp(1) gauge theory by the localization method and confirm such enhancement of the global symmetry at the superconformal limit for $N_f\le 5$ to a few leading orders in the chemical potential. Both perturbative and (anti)instanton contributions are present in this calculation. For $N_f=6,7$ cases some issues related the pole structure of the instanton calculation could not be resolved and here we could provide only some suggestive answer for the leading contributions to the index. For the Sp(N) case, similar issues related to the pole structure appear.Comment: 70 pages, references added, published versio

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

Pragmatism, Education, and the Problem of Pluralism

The concept of pluralism is of central importance in contemporary moral and political education, where a crucial aim is to promote acceptance of the life choices of others and to teach tolerance towards diversity of values. However, this promotion of pluralism suffers from two immediate difficulties. Firstly, the concept of pluralism has proved somewhat elusive, and it is far from clear that its various uses are congruent. Secondly, there is a long-standing criticism against ethical and political pluralism which maintains that pluralist views are difficult if not impossible to defend without succumbing to dreaded relativism. In this article, I will firstly distinguish an educationally interesting form of pluralism and then, drawing from thinkers in the tradition of philosophical pragmatism, attempt to meet the criticism that such pluralism has no interesting philosophical defense.Peer reviewe

Orientifolds and the Refined Topological String

We study refined topological string theory in the presence of orientifolds by counting second-quantized BPS states in M-theory. This leads us to propose a new integrality condition for both refined and unrefined topological strings when orientifolds are present. We define the SO(2N) refined Chern-Simons theory which computes refined open string amplitudes for branes wrapping Seifert three-manifolds. We use the SO(2N) refined Chern-Simons theory to compute new invariants of torus knots that generalize the Kauffman polynomials. At large N, the SO(2N) refined Chern-Simons theory on the three-sphere is dual to refined topological strings on an orientifold of the resolved conifold, generalizing the Gopakumar-Sinha-Vafa duality. Finally, we use the (2,0) theory to define and solve refined Chern-Simons theory for all ADE gauge groups