Steinberg modules and Donkin pairs

We prove that in positive characteristic a module with good filtration for a group of type E6 restricts to a module with good filtration for a subgroup of type F4. (Recall that a filtration of a module for a semisimple algebraic group is called good if its layers are dual Weyl modules.) Our result confirms a conjecture of Brundan for one more case. The method relies on the canonical Frobenius splittings of Mathieu. Next we settle the remaining cases, in characteristic not 2, with a computer-aided variation on the old method of Donkin.Comment: 16 pages; proof of Brundan's conjecture adde

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

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

Ассоциация аллельных полиморфизмов гена эндотелиальной NO-синтазы с развитием ишемической болезни сердца (литературный обзор)

Проведений аналіз вітчизняних та закордонних досліджень стосовно вивчення впливу Т-786С, G894T, 4a/b поліморфізмів гену eNOS на ризик розвитку ІХС у представників різних популяцій. Доведена роль Т-786 С поліморфізма гену eNOS у розвитку ІХС у представників японської, української, італійської популяції, причому в останніх він пов’язаний із багатосудинним ураженням. G894T поліморфізм гену eNOS пов’язаний із підвищеним ризиком розвитку ІХС, ішемічних інсультів в італійській, турецькій, азіатській популяціях, а в російській ─ із рестенозами стентів. Доведений зв’язок 4а/4b поліморфізму гену eNOS із виникненням ІХС у турецькій, японській, корейській, афро-американській, іранській, російській популяціях, а в японській популяції ─ гендерна специфіка даної асоціації. В окремих дослідженнях отримані суперечливі дані щодо впливу Т-786 С поліморфізму гену eNOS в турецькій популяції. Не виявлено асоціації 4а/4b поліморфізму гену eNOS у чоловіків Словенії, Фінляндії, G894T поліморфізму гену eNOS у корейській популяції, а у представників білої австралійської популяцій не виявлено асоціації генотипів 4а/4b, G894T, Т-786С поліморфізму гену eNOS із ризиком розвитку ІХС.В статье проведен анализ отечественных и зарубежных исследований, посвященных изучению влияния Т-786С, G894T, 4a/b полиморфизмов гена eNOS на риск развития ИБС у представителей различных популяций. Доказана роль Т-786 С полиморфизма гена eNOS в развитии ИБС у представителей японской, украинськой, итальянской популяции, причем у последних он связан с многососудистым поражением. G894T полиморфизм гена eNOS связан с повышеным риском развития ИХС, ишемических инсультов в итальянской, турецкой, азиатской популяциях, а в российской ─ с рестенозами стентов. Доказана связь 4а/4b полиморфизма гена eNOS с возникновением ИБС в турецкой, японской, корейской, афро-американской, иранськой, российской популяциях, а в японской популяции ─ гендерная специфика данной ассоциации. В отдельных исследованиях получены противоречивые данные о влиянии Т-786 С полиморфизма гена eNOS в турецкой популяции. Не выявлено ассоциации 4а/4b полиморфизма гена eNOS у мужчин Словении, Финляндии, G894T полиморфизма гена eNOS в корейской популяции, а у представителей белой австралийской популяции не выявлено ассоциации генотипов 4а/4b, G894T, Т-786С полиморфизму гену eNOS с риском развития ИБС.The article analyzed Ukrainian and foreign research on the impact study T-786С, G894T, 4a /b polymorphisms of the eNOS gene on the risk of coronary artery disease (CAD) among representatives of different populations. The role of T-786C polimorphism of the eNOS gene was proven in the development of CAD among Japanese, Ukrainian, Italian population, and in the past it is associated with multivessel disease. G894T polymorphism of the eNOS gene is associated with high risk of CAD, ischemic stroke in Italian, Turkish, Asian populations. In the Russian population this polymorphism assotiated with restenosis of stents. The 4a/4b polymorphism of the eNOS gene has significant influence on risk of CAD in Turkish, Japanese, Korean, AfricanAmerican, Iranian and Russian populations. Japanese population has gender specificity of the association. Conflicting data obtained in separate studies of the influence of T-786C polymorphism of the eNOS gene in the Turkish population. There was no association 4a /4b polymorphism of the eNOS gene in men Slovenia’s men and in Finland. Wasn’t identify association of G894T polymorphism of the eNOS gene in Korean population. Wasn’t detected association of genotypes 4a/4b, G894T, T-786S of the eNOS gene polymorphisms with risk of CAD in white Australians. Due to the existence of common pathogenetic mechanisms, involving NO, polymorphism eNOS gene presence may increases the risk of developing COPD. So perspective is study of polymorphisms eNOS gene in patients with COPD and CAD of Ukrainian population. Investigate their role as candidate genes can help to predict and prevent the appearance of comorbid disorders

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

Predatory Bacteria: A Potential Ally against Multidrug-Resistant Gram-Negative Pathogens

Multidrug-resistant (MDR) Gram-negative bacteria have emerged as a serious threat to human and animal health. Bdellovibrio spp. and Micavibrio spp. are Gram-negative bacteria that prey on other Gram-negative bacteria. In this study, the ability of Bdellovibrio bacteriovorus and Micavibrio aeruginosavorus to prey on MDR Gram-negative clinical strains was examined. Although the potential use of predatory bacteria to attack MDR pathogens has been suggested, the data supporting these claims is lacking. By conducting predation experiments we have established that predatory bacteria have the capacity to attack clinical strains of a variety of ß-lactamase-producing, MDR Gram-negative bacteria. Our observations indicate that predatory bacteria maintained their ability to prey on MDR bacteria regardless of their antimicrobial resistance, hence, might be used as therapeutic agents where other antimicrobial drugs fail. © 2013 Kadouri et al

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

Twistors, Harmonics and Holomorphic Chern-Simons

We show that the off-shell N=3 action of N=4 super Yang-Mills can be written as a holomorphic Chern-Simons action whose Dolbeault operator is constructed from a complex-real (CR) structure of harmonic space. We also show that the local space-time operators can be written as a Penrose transform on the coset SU(3)/(U(1) \times U(1)). We observe a strong similarity to ambitwistor space constructions.Comment: 34 pages, 3 figures, v2: replaced with published version, v3: Added referenc

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