Test of the local form of higher-spin equations via AdS/CFT

The local form of higher-spin equations found recently to the second order [1] is shown to properly reproduce the anticipated $AdS/CFT$ correlators for appropriate boundary conditions. It is argued that consistent $AdS/CFT$ holography for the parity-broken boundary models needs a nontrivial modification of the bosonic truncation of the original higher-spin theory with the doubled number of fields, as well as a nonlinear deformation of the boundary conditions in the higher orders.Comment: 18 pages, Typos and acknowledgement corrected. Misleading notation in Section 4.2 changed. References correcte

Особливості створення ситуації успіху на заняттях з англійської мови у ВНЗ (Creating a situation of success at English classes in a university)

Стаття на тему «Особливості створення ситуації успіху на заняттях з англійської мови у ВНЗ», написана старшим викладачем кафедри іноземних мов Київської державної академії водного транспорту Діденко М.О., описує поняття ситуації успіху, актуальність та значення її створення в процесі навчання. Стаття розглядає результати роботи, спрямованої на створення ситуації успіху, та важливість творчого та диференційованого підходу до студентів як до окремих особистостей та до виконаних ними завдань. Стаття включає практичні поради, яких варто дотримуватись для створення ситуації успіху, мотивації та позитивної атмосфери під час навчання. (The article «Creating a situation of success at English classes in a university» is written by Maria Didenko, a senior teacher of Foreign Languages at Kyiv State Academy of Water Transport. The paper describes the concept of success situation, its relevance and importance in learning process. The article examines the work aimed at creating a situation of success, and the importance of creative and differentiated approach to students as individuals and to the completed tasks. The article includes practical advice, which can be followed to create a situation of success, motivation and positive atmosphere during training.

Charges in nonlinear higher-spin theory

Nonlinear higher-spin equations in four dimensions admit a closed two-form that defines a gauge-invariant global charge as an integral over a two-dimensional cycle. In this paper we argue that this charge gives rise to partitions depending on various lower- and higher-spin chemical potentials identified with modules of topological fields in the theory. The vacuum contribution to the partition is calculated to the first nontrivial order for a solution to higher-spin equations that generalizes AdS4 Kerr black hole of General Relativity. The resulting partition is non-zero being in parametric agreement with the ADM-like behavior of a rotating source. The linear response of chemical potentials to the partition function is also extracted. The explicit unfolded form of 4d GR black holes is given. An explicit formula relating asymptotic higher-spin charges expressed in terms of the generalized higher-spin Weyl tensor with those expressed in terms of Fronsdal fields is obtained.Comment: 23 pages; V3: typos corrected; references and acknowledgement added; example of the topological contribution to spin-4 charge added; new Section 3.1 added establishing relation of our construction for asymptotic charges with the canonical one. Version published in JHE

Lorentz covariant form of extended higher-spin equations

The extension of nonlinear higher-spin equations in d=4 proposed in [arXiv:1504.07289] for the construction of invariant functional is shown to respect local Lorentz symmetry. The equations are rewritten in a manifestly Lorentz covariant form resulting from some Stueckelberg-like field transformation. We also show that the two field-independent central terms entering higher-spin equations which are not entirely fixed by the consistency alone get fixed unambiguously by the requirement of Lorentz symmetry. One of the important advantages of the proposed approach demonstrated in the paper is the remarkable simplification of the perturbative analysis.Comment: V2: 20 pages, typos corrected, references added. Version published in JHE

Free Field Dynamics in the Generalized AdS (Super)Space

Pure gauge representation for general vacuum background fields (Cartan forms) in the generalized $AdS$ superspace identified with $OSp(L,M)$ is found. This allows us to formulate dynamics of free massless fields in the generalized $AdS$ space-time and to find their (generalized) conformal and higher spin field transformation laws. Generic solution of the field equations is also constructed explicitly. The results are obtained with the aid of the star product realization of ortosymplectic superalgebras.Comment: Some notes added, corrected typo

BTZ Black Hole as Solution of 3d Higher Spin Gauge Theory

BTZ black hole is interpreted as exact solution of 3d higher spin gauge theory. Solutions for free massless fields in BTZ black hole background are constructed with the help of the star-product algebra formalism underlying the formulation of 3d higher spin theory. It is shown that a part of higher spin symmetries remains unbroken for special values of the BTZ parameters.Comment: 31 pages, LaTeX; references correcte

Unitarity Bounds in AdS_3 Higher Spin Gravity

We study SL(N,R) Chern-Simons gauge theories in three dimensions. The choice of the embedding of SL(2,R) in SL(N,R), together with asymptotic boundary conditions, defines a theory of higher spin gravity. Each inequivalent embedding leads to a different asymptotic symmetry group, which we map to an OPE structure at the boundary. A simple inspection of these algebras indicates that only the W_N algebra constructed using the principal embedding could admit a unitary representation for large values of the central charge.Comment: 1+23 pages, Version 3 Appendix B revise

Механизмы поляризации в термостабильной БЛТ керамике на сверхвысоких частотах Часть 1: Особенности «жестких» параэлектриков

Розглянуто «жорсткі» параелектрики як матеріал з високою діелектричної проникністю і малими втратами на НВЧ. Описано вплив різних видів поляризації на діелектричні та температурні властивості параелектриків. Описана тетрагональна структура рутила й встановлено вплив кисневих октаедрів TiO₆ на діелектричну проникність параелектриків.The "hard" paraelectrics as a material with a high dielectric constant and low loss at microwave frequencies are considered. The impact of different types of polarization on the dielectric and thermal properties of paraelectric is described. The tetragonal rutile structure is considered and the influence of the oxygen octahedrons TiO₆ on the dielectric constant of the paraelectric is established.Рассмотрены «жесткие» параэлектрики как материал с высокой диэлектрической проницаемостью и малыми потерями на СВЧ. Описано влияние различных видов поляризации на диэлектрические и температурные свойства параэлектриков. Описана тетрагональная структура рутила и установлено влияние кислородных октаэдров TiO₆ на диэлектрическую проницаемость параэлектриков