Quantum symmetries and exceptional collections

We study the interplay between discrete quantum symmetries at certain points in the moduli space of Calabi-Yau compactifications, and the associated identities that the geometric realization of D-brane monodromies must satisfy. We show that in a wide class of examples, both local and compact, the monodromy identities in question always follow from a single mathematical statement. One of the simplest examples is the Z_5 symmetry at the Gepner point of the quintic, and the associated D-brane monodromy identity

C^2/Z_n Fractional branes and Monodromy

We construct geometric representatives for the C^2/Z_n fractional branes in terms of branes wrapping certain exceptional cycles of the resolution. In the process we use large radius and conifold-type monodromies, and also check some of the orbifold quantum symmetries. We find the explicit Seiberg-duality which connects our fractional branes to the ones given by the McKay correspondence. We also comment on the Harvey-Moore BPS algebras.Comment: 34 pages, v1 identical to v2, v3: typos fixed, discussion of Harvey-Moore BPS algebras update

B-type defects in Landau-Ginzburg models

We consider Landau-Ginzburg models with possibly different superpotentials glued together along one-dimensional defect lines. Defects preserving B-type supersymmetry can be represented by matrix factorisations of the difference of the superpotentials. The composition of these defects and their action on B-type boundary conditions is described in this framework. The cases of Landau-Ginzburg models with superpotential W=X^d and W=X^d+Z^2 are analysed in detail, and the results are compared to the CFT treatment of defects in N=2 superconformal minimal models to which these Landau-Ginzburg models flow in the IR.Comment: 50 pages, 2 figure

Triangle-generation in topological D-brane categories

Tachyon condensation in topological Landau-Ginzburg models can generally be studied using methods of commutative algebra and properties of triangulated categories. The efficiency of this approach is demonstrated by explicitly proving that every D-brane system in all minimal models of type ADE can be generated from only one or two fundamental branes.Comment: 34 page

Matrix Factorizations and Homological Mirror Symmetry on the Torus

We consider matrix factorizations and homological mirror symmetry on the torus T^2 using a Landau-Ginzburg description. We identify the basic matrix factorizations of the Landau-Ginzburg superpotential and compute the full spectrum, taking into account the explicit dependence on bulk and boundary moduli. We verify homological mirror symmetry by comparing three-point functions in the A-model and the B-model.Comment: 41 pages, 9 figures, v2: reference added, minor corrections and clarifications, version published in JHE

ПРОВЕРКА ВЗАИМОСВЯЗИ МЕЖДУ ДЕВЯТЬЮ ОДНОНУКЛЕОТИДНЫМИ ПОЛИМОРФИЗМАМИ И ИНФАРКТОМ МИОКАРДА НА СИБИРСКОЙ ПОПУЛЯЦИИ

Aim: to evaluate association between genetic polymorphism (SNPs) and myocardial infarction (identified in recent GWAS) as markers of high risk of myocardial infarction (MI) in Siberian population. Patients were divided into 2 groups — MI patients and control group (ratio 1:2) and presented the sapmle of population of Novosibirsk (9400 patients, 45–69 years) within international project HAPIEE (Health, Alcohol and Psychosocial factors In Eastern Europe). 200 patients with MI (129 men, 71 women) were included. Control group — individuals without MI (420) matched for age and sex. Genomic DNA was extracted from venous blood by phenol-chloroform extraction. Gene polymorphism of genes tested by real-time PCR according to protocol (probes TaqMan, Applied Biosystems, USA) with the use of ABI 7900HT. The following SNPs were studied: rs28711149, rs499818, rs619203, rs10757278 and rs1333049 (hr. 9), rs1376251, rs2549513, rs4804611, rs17465637. The association of SNP and MI was confirmed for 4 of 9 studied SNPs: rs1333049 (hr. 9), rs10757278 (hr. 9), rs499818 (hr. 6), rs619203 gene ROS1. Heart rate was associated with rs1333049 and rs10757278. Glucose level was associated with rs619203, rs28711149 and rs1376251. Total cholesterol and atherogenic index was associated with rs28711149. For the first time in Russian population the associations of GWAS with myocardial infarction SNPs was detected for rs619203, rs499818, rs1333049 and rs10757278. These genetic markers can be used for assessing the risk of myocardial infarction in Russian population. Цель исследования – проверить однонуклеотидные полиморфизмы, идентифицированные в недавних полногеномных ассоциативных исследованиях, на пригодность в качестве маркеров риска развития инфаркта миокарда в сибирской популяции. Группа больных инфарктом миокарда и контрольная группа (соотношение 1:2) были сформированы на основе популяционной выборки 45–69-летних жителей Новосибирска (9400 человек), созданной в рамках международного проекта HAPIEE (Health, Alcohol and Psychosocial factors In Eastern Europe). В исследование было включено 200 больных инфарктом миокарда (129 мужчин, 71 женщина), контрольную группу составили лица без инфаркта (420 человек), сопоставимые по половым и возрастным различиям. Геномную ДНК выделяли из венозной крови методом фенол-хлороформной экстракции. Полиморфизм генов тестировали посредством ПЦР в реальном времени в соответствии с протоколом фирмы производителя (зонды TaqMan, Applied Biosystems, США) на приборе ABI 7900HT. В исследование были включены следующие однонуклеотидные полиморфизмы: rs28711149, rs499818, rs619203, rs10757278 и rs1333049 (хр. 9), rs1376251, rs2549513, rs4804611, rs17465637. Для 4 из 9 исследованных однонуклеотидных полиморфизмов была подтверждена их ассоциация с инфарктом миокарда: rs1333049 (хр. 9), rs10757278 (хр. 9), rs499818 (хр. 6), rs619203 гена ROS1. С частотой сердечных сокращений были взаимосвязаны полиморфизмы rs1333049 и rs10757278, с уровнем глюкозы — rs619203, rs28711149 и rs1376251, с содержанием общего холестерина и индексом атерогенности плазмы — rs28711149. Впервые на российской популяции реплицированы результаты GWAS с инфарктом миокарда ОНП rs619203, rs499818, rs1333049 и rs10757278, Эти генетические маркеры могут использоваться для оценки риска развития инфаркта миокарда на российской популяции.

D-brane superpotentials and RG flows on the quintic

The behaviour of D2-branes on the quintic under complex structure deformations is analysed by combining Landau-Ginzburg techniques with methods from conformal field theory. It is shown that the boundary renormalisation group flow induced by the bulk deformations is realised as a gradient flow of the effective space time superpotential which is calculated explicitly to all orders in the boundary coupling constant.Comment: 24 pages, 1 figure, v2:Typo in (3.14) correcte

On the boundary coupling of topological Landau-Ginzburg models

I propose a general form for the boundary coupling of B-type topological Landau-Ginzburg models. In particular, I show that the relevant background in the open string sector is a (generally non-Abelian) superconnection of type (0,1) living in a complex superbundle defined on the target space, which I allow to be a non-compact Calabi-Yau manifold. This extends and clarifies previous proposals. Generalizing an argument due to Witten, I show that BRST invariance of the partition function on the worldsheet amounts to the condition that the (0,<= 2) part of the superconnection's curvature equals a constant endomorphism plus the Landau-Ginzburg potential times the identity section of the underlying superbundle. This provides the target space equations of motion for the open topological model.Comment: 21 page

Moduli Webs and Superpotentials for Five-Branes

We investigate the one-parameter Calabi-Yau models and identify families of D5-branes which are associated to lines embedded in these manifolds. The moduli spaces are given by sets of Riemann curves, which form a web whose intersection points are described by permutation branes. We arrive at a geometric interpretation for bulk-boundary correlators as holomorphic differentials on the moduli space and use this to compute effective open-closed superpotentials to all orders in the open string couplings. The fixed points of D5-brane moduli under bulk deformations are determined.Comment: 41 pages, 1 figur

Matrix factorisations and D-branes on K3

D-branes on K3 are analysed from three different points of view. For deformations of hypersurfaces in weighted projected space we use geometrical methods as well as matrix factorisation techniques. Furthermore, we study the D-branes on the T^4/\Z_4 orbifold line in conformal field theory. The behaviour of the D-branes under deformations of the bulk theory are studied in detail, and good agreement between the different descriptions is found.Comment: 35 pages, no figure