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

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

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 $\mathbb{P}^{K-1}$

Chiral Algebras of (0,2) Sigma Models: Beyond Perturbation Theory

We explore the nonperturbative aspects of the chiral algebras of N = (0,2) sigma models, which perturbatively are intimately related to the theory of chiral differential operators (CDOs). The grading by charge and scaling dimension is anomalous if the first Chern class of the target space is nonzero. This has some nontrivial consequences for the chiral algebra. As an example, we study the case where the target space is CP^1, and show that worldsheet instantons trivialize the chiral algebra entirely. Consequently, supersymmetry is spontaneously broken in this model. We then turn to a closer look at the supersymmetry breaking from the viewpoint of Morse theory on loop space. We find that instantons interpolate between pairs of perturbative supersymmetric states with different fermionic numbers, hence lifting them out of the supersymmetric spectrum. Our results reveal that a "quantum" deformation of the geometry of the target space leads to a trivialization of the kernels of certain twisted Dirac operators on CP^1.Comment: 38 pages. Minor changes to Section 2.3 and corrections to Section 4.2. Final results unchanged. Typos correcte

Gaudin Model, Bethe Ansatz and Critical Level

We propose a new method of diagonalization of hamiltonians of the Gaudin model associated to an arbitrary simple Lie algebra, which is based on Wakimoto modules over affine algebras at the critical level. We construct eigenvectors of these hamiltonians by restricting certain invariant functionals on tensor products of Wakimoto modules. In conformal field theory language, the eigenvectors are given by certain bosonic correlation functions. Analogues of Bethe ansatz equations naturally appear as Kac-Kazhdan type equations on the existence of certain singular vectors in Wakimoto modules. We use this construction to expalain a connection between Gaudin's model and correlation functions of WZNW models.Comment: 40 pages, postscript-file (references added and corrected

Structure and magnetic properties of the Co2FeAl and Co2NiSi Heusler alloy films

The structural and magnetic properties (field dependences of the magnetization in magnetic fields of up to 6 kOe) of thin-film Co2FeAl, and Co2NiSi Heusler alloys grown by pulsed laser deposition on glass and a single-crystalline Al2O3 R-plane substrate at different growth temperatures (20, 280 and 420 °C) were studied. It was found that the stoichiometric composition of the films depends on the substrate temperature during growth and repeats the composition of the target for films grown at low temperatures. The films deposited on a single crystalline Al2O3 substrate have uniaxial magnetic anisotropy in the plane. © Published under licence by IOP Publishing Ltd.This work was partly supported by the state assignment of Minobrnauki of Russia (themes “Spin” No. АААА-А18-118020290104-2), RFBR grants (Nos. 18-32-00686 and 18-02-00739) and the Government of the Russian Federation (state contract No. 02.A03.21.0006)

ЭФФЕКТИВНОСТЬ РАДИОЧАСТОТНОЙ АБЛАЦИИ УСТЬЕВ ЛЕГОЧНЫХ ВЕН У ПАЦИЕНТОВ С ФИБРИЛЛЯЦИЕЙ ПРЕДСЕРДИЙ И МЕТАБОЛИЧЕСКИМ СИНДРОМОМ

The aim of this study is determination of predictors of efficiency of radiofrequency ablation (RFA) in patients with atrial fibrillation (AF) and metabolic syndrome (MS). Material and methods. 98 patients with AF (78 patients with AF and MS (IDF, 2005) and 20 patients without MS) have been examined. Comparison groups included 50 patients with MS without arrhythmia and 50 practically healthy subjects. RFA was performed with Carto 3 navigation system. Follow-up period after RFA was 12 months. Epicardial fat thickness (EFT) was measured with help of echo-cardiography. Results: patients with AF relapse had more MS components than those with effective procedure (3.21±1.18 and 1.73±1.14, accordingly, p<0.001). Initially, EFT of patients with AF relapse after RFA was larger that in patients without arrhythmia after exposure. EFT in patients with AF more than3.5 mmincreases probability of arrhythmia relapse in 1.87 times (OR: 1.87, 95 % CI 1.03 — 3.41, р = 0.04). Conclusion: determination of EFT with echo-cardiogaphy can be used in estimation of AF relapse risk after RFA.Цель исследования — определение предикторов эффективности радиочастотной аблации (РЧА) у пациентов с фибрилляцией предсердий (ФП) и метаболическим синдромом (МС). Обследованы 98 пациентов с ФП (78 пациентов с ФП и МС (IDF, 2005) и 20 больных без МС. Группы сравнения составили 50 пациентов с МС без аритмии и 50 практически здоровых людей. РЧА выполнялась с помощью навигационной картирующей системы Carto 3. Период наблюдения после РЧА составил 12 месяцев. Толщина эпикардиального жира (ТЭЖ) определена с помощью ЭхоКГ. Число компонентов МС у больных с рецидивом ФП после РЧА больше, чем у больных с эффективной процедурой (3,21±1,18, 1,73±1,14 соответственно, р = 0,001). Исходно ТЭЖ у пациентов с рецидивом ФП после РЧА больше, чем у пациентов без аритмии, после воздействия. ТЭЖ у пациентов с ФП более3,5 ммповышает вероятность рецидива аритмии после РЧА в 1,87 раза (ОШ:1,87, 95 % ДИ 1,03 — 3,41, р = 0,04). Определение ТЭЖ при ЭхоКГ может быть использовано в оценке риска рецидива ФП после РЧА

Finding the Cell Center by a Balance of Dynein and Myosin Pulling and Microtubule Pushing: A Computational Study

By comparing computer modeling predictions with observations, we conclude that strong dynein and weaker myosin-generated forces pull the microtubules inward competing with microtubule plus-ends pushing the microtubule aster outward and that the balance of these forces positions the centrosome at the cell center