Mirror symmetry in two steps: A-I-B

We suggest an interpretation of mirror symmetry for toric varieties via an equivalence of two conformal field theories. The first theory is the twisted sigma model of a toric variety in the infinite volume limit (the A-model). The second theory is an intermediate model, which we call the I-model. The equivalence between the A-model and the I-model is achieved by realizing the former as a deformation of a linear sigma model with a complex torus as the target and then applying to it a version of the T-duality. On the other hand, the I-model is closely related to the twisted Landau-Ginzburg model (the B-model) that is mirror dual to the A-model. Thus, the mirror symmetry is realized in two steps, via the I-model. In particular, we obtain a natural interpretation of the superpotential of the Landau-Ginzburg model as the sum of terms corresponding to the components of a divisor in the toric variety. We also relate the cohomology of the supercharges of the I-model to the chiral de Rham complex and the quantum cohomology of the underlying toric variety.Comment: 50 pages; revised versio

Magnetic force microscopy of epitaxial Fe2CoAl and Co2FeAl Heusler alloy films and microstructures

Research supported by RFBR grant 17-57-45024 IND-a

Analytic Expressions for Singular Vectors of the N=2N=2 Superconformal Algebra

Using explicit expressions for a class of singular vectors of the $N=2$ (untwisted) algebra and following the approach of Malikov-Feigin-Fuchs and Kent, we show that the analytically extended Verma modules contain two linearly independent neutral singular vectors at the same grade. We construct this two dimensional space and we identify the singular vectors of the original Verma modules. We show that in some Verma modules these expressions lead to two linearly independent singular vectors which are at the same grade and have the same charge.Comment: 35 pages, LATE

The Topological Cigar Observables

We study the topologically twisted cigar, namely the SL(2,R)/U(1) superconformal field theory at arbitrary level, and find the BRST cohomology of the topologically twisted N=2 theory. We find a one to one correspondence between the spectrum of the twisted coset and singular vectors in the Wakimoto modules constructed over the SL(2,R) current algebra. The topological cigar cohomology is the crucial ingredient in calculating the closed string spectrum of topological strings on non-compact Gepner models.Comment: 28 page

Two-Dimensional Twisted Sigma Models, the Mirror Chiral de Rham Complex, and Twisted Generalised Mirror Symmetry

In this paper, we study the perturbative aspects of a "B-twisted" two-dimensional $(0,2)$ heterotic sigma model on a holomorphic gauge bundle $\mathcal E$ over a complex, hermitian manifold $X$. We show that the model can be naturally described in terms of the mathematical theory of ``Chiral Differential Operators". In particular, the physical anomalies of the sigma model can be reinterpreted as an obstruction to a global definition of the associated sheaf of vertex superalgebras derived from the free conformal field theory describing the model locally on $X$. In addition, one can also obtain a novel understanding of the sigma model one-loop beta function solely in terms of holomorphic data. At the $(2,2)$ locus, one can describe the resulting half-twisted variant of the topological B-model in terms of a $\it{mirror}$ "Chiral de Rham complex" (or CDR) defined by Malikov et al. in \cite{GMS1}. Via mirror symmetry, one can also derive various conjectural expressions relating the sheaf cohomology of the mirror CDR to that of the original CDR on pairs of Calabi-Yau mirror manifolds. An analysis of the half-twisted model on a non-K\"ahler group manifold with torsion also allows one to draw conclusions about the corresponding sheaves of CDR (and its mirror) that are consistent with mathematically established results by Ben-Bassat in \cite{ben} on the mirror symmetry of generalised complex manifolds. These conclusions therefore suggest an interesting relevance of the sheaf of CDR in the recent study of generalised mirror symmetry.Comment: 97 pages. Companion paper to hep-th/0604179. Published versio

Multiloop Superstring Amplitudes from Non-Minimal Pure Spinor Formalism

Using the non-minimal version of the pure spinor formalism, manifestly super-Poincare covariant superstring scattering amplitudes can be computed as in topological string theory without the need of picture-changing operators. The only subtlety comes from regularizing the functional integral over the pure spinor ghosts. In this paper, it is shown how to regularize this functional integral in a BRST-invariant manner, allowing the computation of arbitrary multiloop amplitudes. The regularization method simplifies for scattering amplitudes which contribute to ten-dimensional F-terms, i.e. terms in the ten-dimensional superspace action which do not involve integration over the maximum number of $\theta$'s.Comment: 23 pages harvmac, added acknowledgemen

Fusion and singular vectors in A1{(1)} highest weight cyclic modules

We show how the interplay between the fusion formalism of conformal field theory and the Knizhnik--Zamolodchikov equation leads to explicit formulae for the singular vectors in the highest weight representations of A1{(1)}.Comment: 42 page

Influence of high-dose ion implantation of NiTi equiatomic on shape memory and pseudoelastic

This work explains the method alloying process of the TiNi thin films in addition to the shape memory properties of the TiNi thin films made by alloying the TiNi multilayer thin films. The surface layer of an equiatomic TiNi alloy, which exhibits the shape memory effect in the martensitic slate, is modified with high-dose implantation ions N⁺, Ni⁺ -N⁺, and Mo⁺ -W⁺ ions at a dose of 10¹⁷ − 10¹⁸ cm⁻² and studied by Rutherford back scattering, scanning electron microscopy, energy dispersive spectroscopy, X-ray diffraction, and by measuring the nanohardness and the elastic modulus. After double implantation ions, the hardness of the TiNi samples is 2.78 ± 0.95 GPa at a depth of 150 nm and 4.95 2.25 GPa at a depth of 50 nm; the elastic modulus is 59 GPa. The coating demonstratedthe increased corrosion resistance in acidic and alkaline media in comparison with that of the non-implanted surface. A correlation between the elemental composition, microstructure, shape memory effect, and mechanical properties of the near-surface layer in TiNi is found.В работе предложен метод модификации свойств тонких пленок TiNi с эффектом памяти формы путем легирования и формирования многослойных пленок. Поверхностный слой эквиатомного сплава TiNi, обладающего эффектом памяти формы в мартенситной фазе, изменялся путем высокодозной имплантации ионов N⁺, Ni⁺ -N⁺ и Mo⁺ -W⁺ с дозой 10¹⁷ − 10¹⁸ см⁻² и исследовался методами Резерфордовского обратного рассеяния, сканирующей электронной микроскопии, энергодисперсионной спектроскопия, дифракции рентгеновских лучей. Дополнительно измерялись нанотвердость и модуль упругости. Обнаружено, что при двойной имплантации ионов микротвердость образцов TiNi составляет 2.78 ± 0.95 ГПа на глубине 150 нм и 4.95 ± 2.25 ГПа на глубине 50 нм, а модуль упругости 59 ГПа. По сравнению с неимплантированной поверхностью покрытие обладает повышенной коррозионной стойкостью в кислых и щелочных средах. Обнаружена корреляция между элементным составом, микроструктурой и эффектом памяти формы и механическими свойствами приповерхностного слоя TiNi.У роботізапропоновано метод модифікації властивостей тонких плівок TiNi з ефектом пам’яті форми шляхом легування та формування багатошарових плівок. Поверхневий шар еквіатомного сплаву TiNi, що має ефект пам’яті форми в мартенситній фазі, змінювався шляхом високодозної імплантації іонів N⁺, Ni⁺ -N⁺ та Mo⁺ -W⁺ з дозою 10¹⁷ − 10¹⁸ см⁻² і досліджувався методами Резерфордівського оберненого розсіювання, скануючої електронноїмікроскопії, енергодисперсійної спектроскопії, дифракції рентгенівських променів. Додатково вимірювалися нанотвердость і модуль пружності. Виявлено, що при подвійний імплантації іонів мікротвердість зразків TiNi становить 2.78 ± 0.95 ГПа на глибині 150 нм та 4.95 ± 2.25 ГПа на глибині 50 нм, а модуль пружності становить 59 ГПа. У порівнянніз неімплантірованною поверхнею покриття має підвищену корозійну стійкість у кислих і лужних середовищах. Виявлено кореляцію міжелементним складом, мікроструктурою та ефектом пам’яті форми і механічними властивостями приповерхневого шару TiNi

Gepner-like models and Landau-Ginzburg/sigma-model correspondence

The Gepner-like models of $k^{K}$-type is considered. When $k+2$ is multiple of $K$ the elliptic genus and the Euler characteristic is calculated. Using free-field representation we relate these models with $\sigma$-models on hypersurfaces in the total space of anticanonical bundle over the projective space $\mathbb{P}^{K-1}$