Unit Killing Vector Fields on Nearly Kahler Manifolds

We study 6-dimensional nearly Kahler manifolds admitting a Killing vector field of unit length. In the compact case it is shown that up to a finite cover there is only one geometry possible, that of the 3--symmetric space $S^3 \times S^3$

The Hypermultiplet with Heisenberg Isometry in N=2 Global and Local Supersymmetry

The string coupling of N=2 supersymmetric compactifications of type II string theory on a Calabi-Yau manifold belongs to the so-called universal dilaton hypermultiplet, that has four real scalars living on a quaternion-Kaehler manifold. Requiring Heisenberg symmetry, which is a maximal subgroup of perturbative isometries, reduces the possible manifolds to a one-parameter family that describes the tree-level effective action deformed by the only possible perturbative correction arising at one-loop level. A similar argument can be made at the level of global supersymmetry where the scalar manifold is hyper-Kaehler. In this work, the connection between global and local supersymmetry is explicitly constructed, providing a non-trivial gravity decoupled limit of type II strings already in perturbation theory.Comment: 24 page

Promoter methylation of cancer-related genes in gastric carcinoma

Genetic changes associated with gastric cancer are not completely known, but epigenetic mechanisms involved in this disease seem to play an important role in its pathophysiology. One of these mechanisms, an aberrant methylation in the promoter regions of genes involved in cancer induction and promotion, may be of particular importance in gastric cancer. Aim: To analyze the methylation status of eight genes: Apaf-1, Casp8, CDH1, MDR1, GSTP1, BRCA1, hMLH1, Fas in gastric cancer patients. Methods: The methylation pattern of the genes was assessed by methylation specific restriction enzyme PCR (MSRE-PCR) in gastric tumors taken during surgery of 27 patients and compared with the methylation pattern in material obtained from biopsy in 25 individuals without cancer and pre-cancerous lesions. Results: We observed a promoter hypermethylation in the Casp8, hMLH1, CDH1 and MDR1 in gastric cancer patients as compared with the controls. Additionally, we investigated the relationship between promoter hypermethylation and age, gender, smoking and gastric cancer family history. The hypermethylation of the hMLH1 gene occurred more frequently in female than in men, and the hypermethylation of the CDH1 gene was observed preferentially in smoking than in non-smoking individuals. Conclusion: The data obtained indicate that changes in DNA methylation may contribute to gastric carcinogenesis.Генетические изменения, ассоциированные с опухолью желудка, изучены не в полной мере. В то же время эпигенетические механизмы скорее всего играют ключевую роль и лежат в основе возникновения этого заболевания. Один из таких механизмов– нарушенияметилирования промоторов генов, которые регулируют злокачественнуютрансформациюи прогрессирование опухолевого процесса, может быть особенно важным в развитии рака желудка. Цель: проанализировать статус метилирования промоторов восьми генов: Apaf-1, Casp8, CDH1, MDR1, GSTP1, BRCA1, hMLH1, Fas у больных раком желудка. Методы: метилирование промоторов генов изучали с помощьюспецифической к сайтамметилирования рестрикцией с ПЦР (MSRE-PCR) на хирургическомматериале (опухоли желудка) 27 пациентов. Вкачестве контроля использовали иопсийныйматериал, полученный от 25 больных, у которых не было выявлено рака или предраковых состояний. Результаты: отмечали гиперметилирование промоторов генов Casp8, hMLH1, CDH1 и MDR1 в опухолевой ткани желудка по сравнению с контрольными образцами. Кроме того, нами была прослежена взаимосвязь между гиперметилированием промоторов генов и возрастом, полом пациентов, курением и семейной историей заболевания раком желудка. Гиперметилирование гена hMLH1 выявляли чаще у женщин, чем у мужчин, а гиперметилирование гена CDH1 — в основном у курильщиков. Выводы: полученные данные свидетельствуют о том, что метилирование ДНК может играть важную роль при развитии рака желудка

On the cohomology of some exceptional symmetric spaces

This is a survey on the construction of a canonical or "octonionic K\"ahler" 8-form, representing one of the generators of the cohomology of the four Cayley-Rosenfeld projective planes. The construction, in terms of the associated even Clifford structures, draws a parallel with that of the quaternion K\"ahler 4-form. We point out how these notions allow to describe the primitive Betti numbers with respect to different even Clifford structures, on most of the exceptional symmetric spaces of compact type.Comment: 12 pages. Proc. INdAM Workshop "New Perspectives in Differential Geometry" held in Rome, Nov. 2015, to appear in Springer-INdAM Serie

Parallel spinors and holonomy groups

In this paper we complete the classification of spin manifolds admitting parallel spinors, in terms of the Riemannian holonomy groups. More precisely, we show that on a given n-dimensional Riemannian manifold, spin structures with parallel spinors are in one to one correspondence with lifts to Spin_n of the Riemannian holonomy group, with fixed points on the spin representation space. In particular, we obtain the first examples of compact manifolds with two different spin structures carrying parallel spinors.Comment: 10 pages, LaTeX2

Holography and Quaternionic Taub-NUT

As a concrete application of the holographic correspondence to manifolds which are only asymptotically Anti-de Sitter, we take a closer look at the quaternionic Taub-NUT space. This is a four dimensional, non-compact, inhomogeneous, riemannian manifold with the interesting property of smoothly interpolating between two symmetric spaces, AdS_4 itself and the coset SU(2,1)/U(2). Even more interesting is the fact that the scalar curvature of the induced conformal structure at the boundary (corresponding to a squashed three-sphere) changes sign as we interpolate between these two limiting cases. Using twistor methods, we construct the bulk-to-bulk and bulk-to-boundary propagators for conformally coupled scalars on quaternionic Taub-NUT. This may eventually enable us to calculate correlation functions in the dual strongly coupled CFT on a squashed S^3 using the standard AdS/CFT prescription.Comment: 1+36 pages, no figures. Some minor typos correcte

HyperK\"ahler quotients and N=4 gauge theories in D=2

We consider certain N=4 supersymmetric gauge theories in D=2 coupled to quaternionic matter multiplets in a minimal way. These theories admit as effective theories sigma-models on non-trivial HyperK\"ahler manifolds obtained as HyperK\"ahler quotients. The example of ALE manifolds is discussed. (Based on a talk given by P. Fr\'e at the F. Gursey Memorial Conference, Istanbul, June 1994).Comment: 22 pages, Latex, no figure

New non compact Calabi-Yau metrics in D=6

A method for constructing explicit Calabi-Yau metrics in six dimensions in terms of an initial hyperkahler structure is presented. The equations to solve are non linear in general, but become linear when the objects describing the metric depend on only one complex coordinate of the hyperkahler 4-dimensional space and its complex conjugated. This situation in particular gives a dual description of D6-branes wrapping a complex 1-cycle inside the hyperkahler space, which was studied by Fayyazuddin. The present work generalize the construction given by him. But the explicit solutions we present correspond to the non linear problem. This is a non linear equation with respect to two variables which, with the help of some specific anzatz, is reduced to a non linear equation with a single variable solvable in terms of elliptic functions. In these terms we construct an infinite family of non compact Calabi-Yau metrics.Comment: A numerical error has been corrected together with the corresponding analysis of the metri

Compact Einstein Spaces based on Quaternionic K\"ahler Manifolds

We investigate the Einstein equation with a positive cosmological constant for $4n+4$-dimensional metrics on bundles over Quaternionic K\"ahler base manifolds whose fibers are 4-dimensional Bianchi IX manifolds. The Einstein equations are reduced to a set of non-linear ordinary differential equations. We numerically find inhomogeneous compact Einstein spaces with orbifold singularity.Comment: LaTeX 28 pages, 5 eps figure

Homogeneous heterotic supergravity solutions with linear dilaton

I construct solutions to the heterotic supergravity BPS-equations on products of Minkowski space with a non-symmetric coset. All of the bosonic fields are homogeneous and non-vanishing, the dilaton being a linear function on the non-compact part of spacetime.Comment: 36 pages; v2 conclusion updated and references adde