A Deformation of Sasakian Structure in the Presence of Torsion and Supergravity Solutions

We discuss a deformation of Sasakian structure in the presence of totally skew-symmetric torsion by introducing odd dimensional manifolds whose metric cones are K\"ahler with torsion. It is shown that such a geometry inherits similar properties to those of Sasakian geometry. As an example of them, we present an explicit expression of local metrics and see how Sasakian structure is deformed by the presence of torsion. We also demonstrate that our example of the metrics admits the existence of hidden symmetries described by non-trivial odd-rank generalized closed conformal Killing-Yano tensors. Furthermore, using these metrics as an {\it ansatz}, we construct exact solutions in five dimensional minimal (un-)gauged supergravity and eleven dimensional supergravity. Finally, we discuss the global structures of the solutions and obtain regular metrics on compact manifolds in five dimensions, which give natural generalizations of Sasaki--Einstein manifolds $Y^{p,q}$ and $L^{a,b,c}$. We also discuss regular metrics on non-compact manifolds in eleven dimensions.Comment: 38 pages, 1 table, v2: version to appear in Class. Quant. Gra

No more CKY two-forms in the NHEK

We show that in the near-horizon limit of a Kerr-NUT-AdS black hole, the space of conformal Killing-Yano two-forms does not enhance and remains of dimension two. The same holds for an analogous polar limit in the case of extremal NUT charge. We also derive the conformal Killing-Yano $p$-form equation for any background in arbitrary dimension in the form of parallel transport.Comment: 36 pages, 12 pdf figures, v2: minor change

New G2 holonomy metrics, D6 branes with inherent U(1)xU(1) isometry and gamma-deformations

It is found the most general local form of the 11-dimensional supergravity backgrounds which, by reduction along one isometry, give rise to IIA supergravity solutions with a RR field and a non trivial dilaton, and for which the condition $F^{(1,1)}=0$ holds. This condition is stronger than the usual condition $F^{ab}J_{ab}=0$, required by supersymmetry. It is shown that these D6 wrapped backgrounds arise from the direct sum of the flat Minkowski metric with certain G2 holonomy metrics admitting an U(1) action, with a local form found by Apostolov and Salamon. Indeed, the strong supersymmetry condition is equivalent to the statement that there is a new isometry on the G2 manifold, which commutes with the old one; therefore these metrics are inherently toric. An example that is asymptotically Calabi-Yau is presented. There are found another G2 metrics which give rise to half-flat SU(3) structures. All this examples possess an U(1)x U(1)x U(1) isometry subgroup. Supergravity solutions without fluxes corresponding to these G2 metrics are constructed. The presence of a $T^3$ subgroup of isometries permits to apply the \gamma-deformation technique in order to generate new supergravity solutions with fluxes.Comment: 29 pages, no figures. References added and corrected. The discussion is minimaly changed and a subtle notational problem was correcte

The Parker Instability in a Thick Gaseous Disk II: Numerical Simulations in 2D

We present 2D, ideal-MHD numerical simulations of the Parker instability in a multi-component warm disk model. The calculations were done using two numerical codes with different algorithms, TVD and ZEUS-3D. The outcome of the numerical experiments performed with both codes is very similar, and confirms the results of the linear analysis for the undular mode derived by Kim et al. (2000): the most unstable wavelength is about 3 kpc and its growth timescale is between 30-50 Myr (the growth rate is sensitive to the position of the upper boundary of the numerical grid). Thus, the time and length scales of this multicomponent disk model are substantially larger than those derived for thin disk models. We use three different types of perturbations, random, symmetric, and antisymmetric, to trigger the instability. The antisymmetric mode is dominant, and determines the minimum time for the onset of the nonlinear regime. The instability generates dense condensations and the final peak column density value in the antisymmetric case, as also derived by Kim et al. (2000), is about a factor of 3 larger than its initial value. These wavelengths and density enhancement factors indicate that the instability alone cannot be the main formation mechanism of giant molecular clouds in the general interstellar medium. The role of the instability in the formation of large-scale corrugations along spiral arms is briefly discussed.Comment: Accepted for publication in ApJ, 20 text pages with 8 figure