New elliptic solutions of the Yang-Baxter equation

We consider finite-dimensional reductions of an integral operator with the elliptic hypergeometric kernel describing the most general known solution of the Yang-Baxter equation with a rank 1 symmetry algebra. The reduced R-operators reproduce at their bottom the standard Baxter's R-matrix for the 8-vertex model and Sklyanin's L-operator. The general formula has a remarkably compact form and yields new elliptic solutions of the Yang-Baxter equation based on the finite-dimensional representations of the elliptic modular double. The same result is also derived using the fusion formalism.Comment: 34 pages, to appear in Commun. Math. Phy

Superconformal indices of three-dimensional theories related by mirror symmetry

Recently, Kim and Imamura and Yokoyama derived an exact formula for superconformal indices in three-dimensional field theories. Using their results, we prove analytically the equality of superconformal indices in some U(1)-gauge group theories related by the mirror symmetry. The proofs are based on the well known identities of the theory of $q$-special functions. We also suggest the general index formula taking into account the $U(1)_J$ global symmetry present for abelian theories.Comment: 17 pages; minor change

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

Continuous wave OSL in bulk AlN single crystals

The kinetics of recombination luminescence of β-irradiated AlN single crystals has been studied with continuous wave optically stimulated luminescence (CW-OSL) method. It is shown that the OSL process is characterized by two exponential components with a decay time τ = 32 and 212 s. Photoionization cross-sections σ = 4.8·10-19 and 7.3·10-20 cm2 have been evaluated, assuming each component is related to electron traps based on VN- and/or ON-centers at various charged states. It is established that dose dependences of the OSL response of the bulk crystals under study are linear with taking into correct accounting for the radiation induced afterglow and hence can be used for quantitative estimates in solid state dosimetry. (© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Infinite elliptic hypergeometric series: convergence and difference equations

We derive finite difference equations of infinite order for theta hypergeometric series and investigate the space of their solutions. In general, such infinite series diverge, we describe some constraints on the parameters when they do converge. In particular, we lift the Hardy-Littlewood criterion on the convergence of $q$-hypergeometric series for $|q|=1, \, q^n\neq 1$, to the elliptic level and prove convergence of the infinite ${}_{r+1}V_r$ very-well poised elliptic hypergeometric series for restricted values of $q$.Comment: 24 pp, to appear in "Sbornik: Mathematics

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

q-Ultraspherical polynomials for q a root of unity

Properties of the $q$-ultraspherical polynomials for $q$ being a primitive root of unity are derived using a formalism of the $so_q(3)$ algebra. The orthogonality condition for these polynomials provides a new class of trigonometric identities representing discrete finite-dimensional analogs of $q$-beta integrals of Ramanujan.Comment: 7 pages, LATE