Invariant solutions to the Strominger system and the heterotic equations of motion

We construct many new invariant solutions to the Strominger system with respect to a 2-parameter family of metric connections $\nabla^{\varepsilon,\rho}$ in the anomaly cancellation equation. The ansatz $\nabla^{\varepsilon,\rho}$ is a natural extension of the canonical 1-parameter family of Hermitian connections found by Gauduchon, as one recovers the Chern connection $\nabla^{c}$ for $({\varepsilon,\rho})=(0,\frac12)$, and the Bismut connection $\nabla^{+}$ for $({\varepsilon,\rho})=(\frac12,0)$. In particular, explicit invariant solutions to the Strominger system with respect to the Chern connection, with non-flat instanton and positive $\alpha'$ are obtained. Furthermore, we give invariant solutions to the heterotic equations of motion with respect to the Bismut connection. Our solutions live on three different compact non-K\"ahler homogeneous spaces, obtained as the quotient by a lattice of maximal rank of a nilpotent Lie group, the semisimple group SL(2,$\mathbb{C}$) and a solvable Lie group. To our knowledge, these are the only known invariant solutions to the heterotic equations of motion, and we conjecture that there is no other such homogeneous space admitting an invariant solution to the heterotic equations of motion with respect to a connection in the ansatz $\nabla^{\varepsilon,\rho}$.Comment: 27 pages, 3 figure

The ascending central series of nilpotent Lie algebras with complex structure

We obtain several restrictions on the terms of the ascending central series of a nilpotent Lie algebra $\mathfrak g$ under the presence of a complex structure $J$. In particular, we find a bound for the dimension of the center of $\mathfrak g$ when it does not contain any non-trivial $J$-invariant ideal. Thanks to these results, we provide a structural theorem describing the ascending central series of 8-dimensional nilpotent Lie algebras $\mathfrak g$ admitting this particular type of complex structures $J$. Since our method is constructive, it allows us to describe the complex structure equations that parametrize all such pairs $(\mathfrak g, J)$.Comment: 28 pages, 1 figure. To appear in Trans. Amer. Math. So

Symplectically harmonic cohomology of nilmanifolds

This paper can be considered as an extension to our paper [On symplectically harmonic forms on six-dimensional nilmanifolds, Comment. Math. Helv. 76 (2001), n 1, 89-109]. Also, it contains a brief survey of recent results on symplectically harmonic cohomology.Comment: 18 page

A young stellar environment for the superluminous supernova PTF12dam

The progenitors of super luminous supernovae (SLSNe) are still a mystery. Hydrogen-poor SLSN hosts are often highly star-forming dwarf galaxies and the majority belongs to the class of extreme emission line galaxies hosting young and highly star-forming stellar populations. Here we present a resolved long-slit study of the host of the hydrogen-poor SLSN PTF12dam probing the kpc environment of the SN site to determine the age of the progenitor. The galaxy is a "tadpole" with uniform properties and the SN occurred in a star-forming region in the head of the tadpole. The galaxy experienced a recent star-burst superimposed on an underlying old stellar population. We measure a very young stellar population at the SN site with an age of ~3 Myr and a metallicity of 12+log(O/H)=8.0 at the SN site but do not observe any WR features. The progenitor of PTF12dam must have been a massive star of at least 60 M_solar and one of the first stars exploding as a SN in this extremely young starburst.Comment: submitted to MNRAS letters. 5 pages, 3 figures, supplementary material: 2 figures, 2 table

CDS wide slit time-series of EUV coronal bright points

Wide slit (90" x 240" ) movies of four Extreme Ultraviolet coronal bright points (BPs) obtained with the Coronal Diagnostic Spectrometer (CDS) on board the Solar and Heliospheric Observatory (SoHO) have been inspected. The wavelet analysis of the He I 584.34 Å, O V 629.73 Å and Mg VII/IX 368 Å time-series confirms the oscillating nature of the BPs, with periods ranging between 600 and 1100 s. In one case we detect periods as short as 236 s. We suggest that these oscillations are the same as those seen in the chromospheric network and that a fraction of the network bright points are most likely the cool footpoints of the loops comprising coronal bright points. These oscillations are interpreted in terms of global acoustic modes of the closed magnetic structures associated with BPs

The Temperature Dependence of Solar Active Region Outflows

Spectroscopic observations with the EUV Imaging Spectrometer (EIS) on Hinode have revealed large areas of high speed outflows at the periphery of many solar active regions. These outflows are of interest because they may connect to the heliosphere and contribute to the solar wind. In this Letter we use slit rasters from EIS in combination with narrow band slot imaging to study the temperature dependence of an active region outflow and show that it is more complicated than previously thought. Outflows are observed primarily in emission lines from Fe XI - Fe XV. Observations at lower temperatures (Si VII), in contrast, show bright fan-like structures that are dominated by downflows. The morphology of the outflows is also different than that of the fans. This suggests that the fan loops, which often show apparent outflows in imaging data, are contained on closed field lines and are not directly related to the active region outflows.Comment: Movies are available online at: http://tcrb.nrl.navy.mil/~hwarren/temp/papers/flow_temperatures/ To be submitted to ApJ

Is Small Perfect? Size Limit to Defect Formation in Pyramidal Pt Nanocontacts

We report high resolution transmission electron microscopy and ab initio calculation results for the defect formation in Pt nanocontacts (NCs). Our results show that there is a size limit to the existence of twins (extended structural defects). Defects are always present but blocked away from the tip axes. The twins may act as scattering plane, influencing contact electron transmission for Pt NC at room temperature and Ag/Au NC at low temperature.Comment: 4 pages, 3 figure

On the real homotopy type of generalized complex nilmanifolds

We prove that for any n = 4, there are infinitely many real homotopy types of 2n-dimensional nilmanifolds admitting generalized complex structures of every type k, for 0 = k = n