N=2 Sigma Model with Twisted Mass and Superpotential: Central Charges and Solitons

We consider supersymmetric sigma models on the Kahler target spaces, with twisted mass. The Kahler spaces are assumed to have holomorphic Killing vectors. Introduction of a superpotential of a special type is known to be consistent with N=2 superalgebra (Alvarez-Gaume and Freedman). We show that the algebra acquires central charges in the anticommutators {Q_L, Q_L} and {Q_R, Q_R}. These central charges have no parallels, and they can exist only in two dimensions. The central extension of the N=2 superalgebra we found paves the way to a novel phenomenon -- spontaneous breaking of a part of supersymmetry. In the general case 1/2 of supersymmetry is spontaneously broken (the vacuum energy density is positive), while the remaining 1/2 is realized linearly. In the model at hand the standard fermion number is not defined, so that the Witten index as well as the Cecotti-Fendley-Intriligator-Vafa index are useless. We show how to construct an index for counting short multiplets in internal algebraic terms which is well-defined in spite of the absence of the standard fermion number. Finally, we outline derivation of the quantum anomaly in {\bar Q_L, Q_R}.Comment: 21 pages, Latex, 1 eps figure. Two important references adde

Issues in Topological Gauge Theory

We discuss topological theories, arising from the general $\mathcal{N}=2$ twisted gauge theories. We initiate a program of their study in the Gromov-Witten paradigm. We re-examine the low-energy effective abelian theory in the presence of sources and study the mixing between the various $p$-observables. We present the twisted superfield formalism which makes duality transformations transparent. We propose a scheme which uniquely fixes all the contact terms. We derive a formula for the correlation functions of $p$-observables on the manifolds of generalized simple type for $0 \leq p \leq 4$ and on some manifolds with $b_{2}^{+} =1$. We study the theories with matter and explore the properties of universal instanton. We also discuss the compactifications of higher dimensional theories. Some relations to sigma models of type $A$ and $B$ are pointed out and exploited.Comment: 72 pp., Harvmac (b) mode, some typos corrected, reference adde

On Microscopic Origin of Integrability in Seiberg-Witten Theory

We discuss microscopic origin of integrability in Seiberg-Witten theory, following mostly the results of hep-th/0612019, as well as present their certain extension and consider several explicit examples. In particular, we discuss in more detail the theory with the only switched on higher perturbation in the ultraviolet, where extra explicit formulas are obtained using bosonization and elliptic uniformization of the spectral curve.Comment: 24 pages, 1 figure, LaTeX, based on the talks at 'Geometry and Integrability in Mathematical Physics', Moscow, May 2006; 'Quarks-2006', Repino, May 2006; Twente conference on Lie groups, December 2006 and 'Classical and Quantum Integrable Models', Dubna, January 200

СОРБЦИОННОЕ РАЗДЕЛЕНИЕ Fe(III)/Fe(II) И ИХ АЭС-ИСП ОПРЕДЕЛЕНИЕ С ИСПОЛЬЗОВАНИЕМ КРЕМНЕЗЕМА, МОДИФИЦИРОВАННОГО ТАЙРОНОМ

Silica that was sequentially modified with polyhexamethylene guanidine and pyrocatechin-3,5-disulfonic acid (SiO2-PHMG-Tiron) was suggested for the sorption separation and determination of Fe(III) and Fe(II). It was found that the quantitative extraction of Fe(III) was attained at pH 2.5–4.0, while the quantitative extraction of Fe(II) was observed at pH 6.0–7.5. The time of attainment of the sorption equilibrium was less than 5 min. Solid-phase extraction in flow on-column allowed for the quantitative separation and pre-concentration of Fe(III) at pH 3.0, and Fe(II) at pH 6.0–7.0 respectively. Dynamic sorption capacity of SiO2-PHMG-Tiron for Fe(III) was 1.5 mg/g and 1.1 mg/g for Fe(II). The optimal flow rate was 1.5 mL/min. Iron was desorbed from the SiO2-PHMG-Tiron surface by passing 10 mL of 0.5M HNO3 or 5 mL of 1 М HNO3 with the flow rate of 1 mL/min. The procedures for the separation of Fe(III) and Fe(II) followed by the inductively coupled plasma optical emission determination in desorbing solutions using single-column or two-column version were suggested. The single-column version comprised of pre-concentration of Fe(III) at pH 3.0 in the mini-column, determination of Fe(II) in the effluent solution, desorption of Fe(III), and its ICP-АES determination in the desorbing solution. In the two-column version, the analyzed water sample was passed through the two-column system. In the first one, Fe(III) was adsorbed at pH 3.0, in the second one Fe(II) was adsorbed at pH 6.0. Adsorbed iron was desorbed from the columns separately by passing 10 mL portions of 0.5M HNO3 through each column, and iron content in each of them was then determined. The developed procedure was applied for the determination of Fe(II) and Fe(III) in natural waters.Keywords: separation of Fe(II) and Fe(III), solid-phase extraction, silica, Tiron, ICP-АES(Russian)DOI: http://dx.doi.org/10.15826/analitika.2017.21.4.002Didukh S.L., Losev V.N. Scientific research engineering centre “Kristall” Siberian Federal University, 660041, Svobodnyi av. 79, Krasnoyarsk, Russian FederationДля сорбционного разделения и определения Fe(III) и Fe(II) предложен кремнезем, последовательно модифицированный полигексаметиленгуанидином (ПГМГ) и пирокатехин-3,5-дисульфокислотой (тайрон) (сорбент SiO2–ПГМГ–тайрон). Показано, что сорбент количественно извлекает Fe(III) из растворов с рН = 2.5-4.0, а Fe(II) с рН = 6.0-7.5 при времени установления сорбционного равновесия, не превышающем 5 минут. Использование динамического режима позволяет количественно отделить и сконцентрировать Fe(III) при рН = 3.0, а Fe(II) при рН = 6.0-7.0. Динамическая сорбционная емкость SiO2–ПГМГ–тайрон по Fe(III) составляет 1.5 мг/г, по Fe(II) – 1.1 мг/г. Оптимальная скорость потока раствора 1.5 мл/мин. Железо десорбируется с поверхности SiO2–ПГМГ–тайрон при пропускании 10 мл 0.5 М HNO3 или 5 мл 1 М HNO3 со скоростью 1 мл/мин. Предложены методики разделения Fe(III) и Fe(II) и их последующего атомно-эмиссионного с индуктивно связанной плазмой (АЭС-ИСП) определения в десорбирующих растворах с использованием одноколоночного и двухколоночного варианта. Одноколоночный вариант включает сорбционное концентрирование Fe(III) при рН = 3.0 в миниколонке, определение Fe(II) в прошедшем через миниколонку растворе, десорбцию Fe(III) и его АЭС-ИСП определение в десорбирующем растворе. В двухколоночном варианте анализируюмую воду пропускают через систему двух миниколонок. В первой миниколонке при рН = 3.0 сорбируется Fe(III), а во второй при рН = 6.0 – Fe(II). Сорбированное железо десорбируют раздельно с каждой колонки пропусканием по 10 мл 0.5 М HNO3 и определяют в них содержание железа. Разработанная методика апробирована при определении Fe(II) и Fe(III) в природных скваженных водах.Ключевые слова: разделение  Fe(II) и Fe(III), сорбционное концентрирование, кремнезем, тайрон, АЭС-ИСПDOI: http://dx.doi.org/10.15826/analitika.2017.21.4.00

СОРБЦИОННО-ФОТОМЕТРИЧЕСКОЕ И ТЕСТ-ОПРЕДЕЛЕНИЕ МЕДИ В ВОДНЫХ СРЕДАХ С ПРИМЕНЕНИЕМ МОДИФИЦИРОВАННЫХ ПОЛИГЕКСАМЕТИЛЕНГУАНИДИНОМ И БАТОКУПРОИНДИСУЛЬФОКИСЛОТОЙ НЕОРГАНИЧЕСКИХ ОКСИДОВ

Adsorbents based on aluminium, zirconium and titanium oxides sequentially modified with polyhexamethylene guanidine (PHMG) and bathocuproinedisulfonic acid (Batocuprsulfo) were proposed for the adsorption-photometric and test-determination of copper in the variant of test tubes. An effective reagent fixation on the surface of inorganic oxides preliminarily modified with PHMG was attained in the range of pH 3-7. The adsorption capacity of the adsorbents for Batocuprsulfo was 22, 11, 7 mmol/g for Al2O3, ZrO2, and TiO2, respectively. Complex compound of Cu(I) with Batocuprsulfo and stoichiometry Cu:Batocuprsulfo=1:2 was formed on the adsorbents surface during Cu(II) adsorption in the presence of reducing agent – hydroxylamine; it was orange colored with maximum at 490 nm in the diffuse reflectance spectra. The quantitative extraction of Cu(I) and the maximum intensity of the surface color of Cu(I) complex was attained from the solutions with pH 6.0–7.0. This effect was used for developing the procedures for adsorption-photometric determination of Cu(I). The most sensitive procedure used aluminium oxide as an adsorbent matrix. The detection limit of Cu(I) determination calculated by the 3s-criterion was 0.02 μg/0.1 g of the adsorbent. The calibration curves were linear over the range of 0.1 - 15.0 μg/0.1 g. The test-procedure for determination of copper by the length of colored area was developed. The minimum determined concentration of copper was 2 mg/L. The proposed methods were used for the determination of Cu(I) in mineral and natural waters. The results obtained were confirmed by the added−found method, and the results of atomic-emission method with inductively coupled plasma.Key words: copper(II), adsorption, inorganic oxides, modified, bathocuproinedisulfonic acid, diffuse reflectance spectroscopy, test determination(Russian)DOI: http://dx.doi.org/10.15826/analitika.2017.21.1.005Didukh S.L., Losev V.N. Scientific research engineering centre “Kristall” Siberian Federal University,Svobodnyi pr.,  79, Krasnoiarsk, 660041, Russian FederationДля сорбционно-фотометрического и тест-определения меди в варианте индикаторных трубок предложены сорбенты на основе оксидов алюминия, циркония и титана, последовательно модифицированных полигексаметиленгуанидином (ПГМГ) и батокупроиндисульфокислотой (Batocuprsulfo). Эффективное закрепление реагента на поверхности неорганических оксидов, предварительно модифицированных ПГМГ, достигается в диапазоне рН = 3.0-7.0. Максимальная поверхностная концентрация Batocuprsulfo на поверхности неорганических оксидов, модифицированных ПГМГ, составляет 22, 11 и 7 мкмоль/г для Al2O3, ZrO2 и TiO2 соответственно. При сорбции Cu(II) в присутствии восстановителя (гидроксиламина гидрохлорида) на поверхности сорбентов образуется комплекс Cu(I) : Batocuprsulfo = 1 : 2, имеющий оранжевую окраску и максимум при 490 нм в спектрах диффузного отражения. Количественное извлечение Cu(I) неорганическими оксидами, модифицированными ПГМГ и Batocuprsulfo, достигается из растворов с рН = 6.0-7.0 и не зависит от природы матрицы сорбента. Максимальная интенсивность окраски поверхностного комплекса Cu(I) сохраняется в диапазоне рН = 6.0-7.0. Образование окрашенных комплексов Cu(I) на поверхности сорбентов использовано при разработке методик его сорбционно-фотометрического определения с использованием спектроскопии диффузного отражения. Наибольшей чувствительностью характеризуется методика с использованием в качестве матрицы сорбента оксида алюминия. Предел обнаружения Cu(I), рассчитанный по 3s-критерию, равен 0.02 мкг/0.1 г сорбента. Линейность градуировочного графика сохраняется в диапазоне 0.1-15.0 мкг Cu на 0.1 г сорбента. С использованием оксида алюминия, модифицированного ПГМГ и Batocuprsulfo, в качестве тест-системы разработана методика тест-определения меди в природных водах по длине окрашенной зоны с минимально определяемой концентрацией меди 2 мкг/л. Правильность методик подтверждена методом «введено-найдено» и сопоставлением с результатами, полученными независимым методом – АЭС-ИСП.Ключевые слова: медь, сорбционное концентрирование, неорганические оксиды, модифицирование, батокупроиндисульфокислота, сорбционно-фотометрическое определение, тест-определениеDOI: http://dx.doi.org/10.15826/analitika.2017.21.1.00

S-duality and Topological Strings

In this paper we show how S-duality of type IIB superstrings leads to an S-duality relating A and B model topological strings on the same Calabi-Yau as had been conjectured recently: D-instantons of the B-model correspond to A-model perturbative amplitudes and D-instantons of the A-model capture perturbative B-model amplitudes. Moreover this confirms the existence of new branes in the two models. As an application we explain the recent results concerning A-model topological strings on Calabi-Yau and its equivalence to the statistical mechanical model of melting crystal.Comment: 13 page

Conical refraction of a high-M2 laser beam

We report on experiments with conical refraction of laser beams possessing a high beam propagation parameter M2. With beam propagation parameter values M2=3 and M2=5, unusual Lloyd's distributions with correspondingly three and five dark rings were observed. In order to explain this phenomenon, we extend the dual-cone model of the conical refraction that describes it as a product of interference of two cones that converge and diverge behind the exit facet of the crystal. In the extended model, these converging/diverging cones are represented as the cone-shaped quasi-Gaussian beams possessing the M2 parameter of an original beam. In this formalism, a beam-waist of these cone-shaped beams is proportional to the M2 value and defines the area of their interference which is a width of the Lloyd's ring. Therefore, the number of dark rings in the Lloyd distribution is defined by the M2 value and can be much greater than unity. The results of the numerical simulations within the extended dual-cone model are in excellent agreement with the experiment