On a modular property of N=2 superconformal theories in four dimensions

In this note we discuss several properties of the Schur index of N=2 superconformal theories in four dimensions. In particular, we study modular properties of this index under SL(2,Z) transformations of its parameters.Comment: 23 page, 2 figure

Study of the luminescence properties of the oxygen-vacancy centers in irradiated AlN single crystals

Целью работы является изучение механизмов люминесценции с участием дефектных комплексов на основе кислородных примесей и азотных вакансий в нит-риде алюминия после воздействия ионизирующего излучения. Для достижения поставленной цели были решены следующие задачи: определены спектральные и кинетические параметры для различных механизмов стимуляции в образцах; получены фундаментальные данные о центрах свечения и механизмах люминесценции в объемных монокристаллах AlN; проведена оценка дозиметрических параметров монокристаллов AlN при использовании методик оптически стимулированной люминесценции. Выполнение заявленных исследований материалов на основе монокристаллического нитрида алюминия позволило получить новые научные результаты, которые могут быть использованы при создании более совершенных детекторов для различных задач персональной и технической дозиметрии ионизирующих излучений. Результаты работы представлены на XIV-ой Всероссийской школы-семинара по проблемам физики конденсированного состояния вещества (Екатеринбург, 2013). В настоящий момент готовится 1 статья для публикации в одном из реферируемых иностранных журналов. Кроме того в рамках выполнения научно-исследовательской работы были получены дополнительные экспериментальные данные, которые позволили написать одну из глав диссертации.The aim is to study the luminescence mechanisms with participation of the defect complexes on the basis of oxygen impurities and nitrogen vacancies in the aluminum nitride after exposure to ionizing radiation. To achieve this purpose the following objectives have been solved: defined spectral and kinetic parameters for the different mechanisms of lumines-cence in the samples; obtained fundamental data on the luminescence centers and mechanisms of luminescence in AlN bulk single crystals; evaluated the dosimetric parameters of AlN single crystals by using optically stimulated luminescence techniques. Performance of applications for studies of materials based on aluminum nitride single crystal provided new scientific results that can be used to create improveddetectors for different tasks personal and technical dosimetry of ionizing radiation. The results of the work presented at the XIV All-Russian seminar on condensed matter physics (Ekaterinburg, 2013 ). Currently preparing one article for publication in a peer-reviewed international journal. Also as part of the research work has yielded experi-mental data that allowed to write one of the dissertation chapters.Программа развития УрФУ на 2013 год (п.2.1.1.1

S-duality and 2d Topological QFT

We study the superconformal index for the class of N=2 4d superconformal field theories recently introduced by Gaiotto. These theories are defined by compactifying the (2,0) 6d theory on a Riemann surface with punctures. We interpret the index of the 4d theory associated to an n-punctured Riemann surface as the n-point correlation function of a 2d topological QFT living on the surface. Invariance of the index under generalized S-duality transformations (the mapping class group of the Riemann surface) translates into associativity of the operator algebra of the 2d TQFT. In the A_1 case, for which the 4d SCFTs have a Lagrangian realization, the structure constants and metric of the 2d TQFT can be calculated explicitly in terms of elliptic gamma functions. Associativity then holds thanks to a remarkable symmetry of an elliptic hypergeometric beta integral, proved very recently by van de Bult.Comment: 25 pages, 11 figure

Comparative analysis of the old and new versions of GOST 7.32

On July 1, 2018, a new edition of GOST 7.32–2017 «The Report on Scientific Research. Structure and rules of registration». Modern possibilities of document circulation in electronic and paper form and updated requirements for design are presented in this version. In this article, the distinctive features of the old and new versions of the standard are presentedС 1 июля 2018 года в силу вступает новая редакция ГОСТ 7.32–2017 «Отчет о научно-исследовательской работе. Структура и правила оформления». В указанной версии учтены современные возможности документооборота в электронном и бумажном виде, актуализированы и дополнены существующие требования к оформлению. В настоящей работе приведены отличительные черты старой и новой редакций стандарт

Systems with Higher-Order Shape Invariance: Spectral and Algebraic Properties

We study a complex intertwining relation of second order for Schroedinger operators and construct third order symmetry operators for them. A modification of this approach leads to a higher order shape invariance. We analyze with particular attention irreducible second order Darboux transformations which together with the first order act as building blocks. For the third order shape-invariance irreducible Darboux transformations entail only one sequence of equidistant levels while for the reducible case the structure consists of up to three infinite sequences of equidistant levels and, in some cases, singlets or doublets of isolated levels.Comment: 18 pages, LaTeX, editorial page is remove

Index for Three Dimensional Superconformal Field Theories and Its Applications

We review aspects of superconformal indices in three dimension. Three dimensional superconformal indices can be exactly computed by using localization method including monopole contribution, and can be applied to provide evidences for mirror duality, AdS_4/CFT_3 correspondence and global symmetry enhancement of strongly coupled gauge theories. After reviewing, we discuss the possibility of global symmetry enhancement in a finite rank of gauge group.Comment: 14 pages, Proceedings of the Seventh International Conference Quantum Theory and Symmetries (QTS-7) in Prague, Czech Republic, August, 2011; v2: minor modifications, discussion of supersymmetry enhancement of abelian ABJM theory by using an index were adde

Spectrally resolved thermoluminescence in UV excited hexagonal boron nitride nanopowder

Thermally stimulated luminescence (TSL) excitation and emission processes in h-BN nanopowders after UV irradiation were studied. TSL showed the highest response within the 5.4 eV band. 3.0 and 3.9 eV bands, resulting from the radiative donor-acceptor recombination between the electron (1B-H O N -centers) and the hole traps (CN-center), were found. TSL curves quantitative analysis in the context of general order kinetics was made. It was shown that 1B-centers had 0.850.05 eV activation energy and were responsible for the TSL peak at 35010 K. Band structure for TSL excitation and emission mechanisms in h-BN nanopowder was suggested. © Published under licence by IOP Publishing Ltd