Flat Symplectic Bundles of N-Extended Supergravities, Central Charges and Black-Hole Entropy

In these lectures we give a geometrical formulation of N-extended supergravities which generalizes N=2 special geometry of N=2 theories. In all these theories duality symmetries are related to the notion of "flat symplectic bundles" and central charges may be defined as "sections" over these bundles. Attractor points giving rise to "fixed scalars" of the horizon geometry and Bekenstein-Hawking entropy formula for extremal black-holes are discussed in some details.Comment: Based on lectures given by S. Ferrara at the 5th Winter School on Mathematical Physics held at the Asia Pacific Center for Theoretical Physics, Seul (Korea), February 199

Galaxies into the Dark Ages

We consider the capabilities of current and future large facilities operating at 2\,mm to 3\,mm wavelength to detect and image the [CII] 158\,$\mu$m line from galaxies into the cosmic "dark ages" ($z \sim 10$ to 20). The [CII] line may prove to be a powerful tool in determining spectroscopic redshifts, and galaxy dynamics, for the first galaxies. We emphasize that the nature, and even existence, of such extreme redshift galaxies, remains at the frontier of open questions in galaxy formation. In 40\,hr, ALMA has the sensitivity to detect the integrated [CII] line emission from a moderate metallicity, active star-forming galaxy [$Z_A = 0.2\,Z_{\odot}$; star formation rate (SFR) = 5\,$M_\odot$\,yr$^{-1}$], at $z = 10$ at a significance of 6$\sigma$. The next-generation Very Large Array (ngVLA) will detect the integrated [CII] line emission from a Milky-Way like star formation rate galaxy ($Z_{A} = 0.2\,Z_{\odot}$, SFR = 1\,$M_\odot$\,yr$^{-1}$), at $z = 15$ at a significance of 6$\sigma$. Imaging simulations show that the ngVLA can determine rotation dynamics for active star-forming galaxies at $z \sim 15$, if they exist. Based on our very limited knowledge of the extreme redshift Universe, we calculate the count rate in blind, volumetric surveys for [CII] emission at $z \sim 10$ to 20. The detection rates in blind surveys will be slow (of order unity per 40\,hr pointing). However, the observations are well suited to commensal searches. We compare [CII] with the [OIII] 88$\mu$m line, and other ancillary information in high $z$ galaxies that would aid these studies.Comment: 11pages, 8 figures, Accepted for the Astrophysical Journa

F^4 Terms in N=4 String Vacua

We discuss $F_{\mu\nu}^4$ terms in torroidal compactifications of type-I and heterotic SO(32) string theory. We give a simple argument why only short BPS multiplets contribute to these terms at one loop, and verify heterotic-type-I duality to this order.Comment: 10 pages, Latex. A statement about superinvariants was corrected. Minor cosmetic changes were also made. To appear in Proceedings of Trieste Spring School and Workshop, April 199

Multiplet Structures of BPS Solitons

There exist simple single-charge and multi-charge BPS p-brane solutions in the D-dimensional maximal supergravities. From these, one can fill out orbits in the charge vector space by acting with the global symmetry groups. We give a classification of these orbits, and the associated cosets that parameterise them.Comment: Latex, 34 pages, comments and reference adde

CO line emission from galaxies in the Epoch of Reionization

We study the CO line luminosity ($L_{\rm CO}$), the shape of the CO Spectral Line Energy Distribution (SLED), and the value of the CO-to-$\rm H_2$ conversion factor in galaxies in the Epoch of Reionization (EoR). To this aim, we construct a model that simultaneously takes into account the radiative transfer and the clumpy structure of giant molecular clouds (GMCs) where the CO lines are excited. We then use it to post-process state-of-the-art zoomed, high resolution ($30\, \rm{pc}$), cosmological simulation of a main-sequence ($M_{*}\approx10^{10}\, \rm{M_{\odot}}$, $SFR\approx 100\,\rm{M_{\odot}\, yr^{-1}}$) galaxy, "Alth{\ae}a", at $z\approx6$. We find that the CO emission traces the inner molecular disk ($r\approx 0.5 \,\rm{kpc}$) of Alth{\ae}a with the peak of the CO surface brightness co-located with that of the [CII] 158$\rm \mu m$ emission. Its $L_{\rm CO(1-0)}=10^{4.85}\, \rm{L_{\odot}}$ is comparable to that observed in local galaxies with similar stellar mass. The high ($\Sigma_{gas} \approx 220\, \rm M_{\odot}\, pc^{-2}$) gas surface density in Alth{\ae}a, its large Mach number (\mach$\approx 30$), and the warm kinetic temperature ($T_{k}\approx 45 \, \rm K$) of GMCs yield a CO SLED peaked at the CO(7-6) transition, i.e. at relatively high-$J$, and a CO-to-$\rm H_2$ conversion factor $\alpha_{\rm CO}\approx 1.5 \, \rm M_{\odot} \rm (K\, km\, s^{-1}\, pc^2)^{-1}$ lower than that of the Milky Way. The ALMA observing time required to detect (resolve) at 5$\sigma$ the CO(7-6) line from galaxies similar to Alth{\ae}a is $\approx13$ h ($\approx 38$ h).Comment: 16 pages, 14 figures, accepted for publication in MNRA

Very extended cold gas, star formation and outflows in the halo of a bright QSO at z>6

Past observations of QSO host galaxies at z >6 have found cold gas and star formation on compact scales of a few kiloparsecs. We present new high sensitivity IRAM PdBI follow-up observations of the [CII] 158micron emission line and FIR continuum in the host galaxy of SDSS J1148+5152, a luminous QSO at redshift 6.4189. We find that a large fraction of the gas traced by [CII] is at high velocities, up to ~1400 km/s relative to the systemic velocity, confirming the presence of a major quasar-driven outflow indicated by previous observations. The outflow has a complex morphology and reaches a maximum projected radius of ~30 kpc. The extreme spatial extent of the outflow allows us, for the first time in an external galaxy, to estimate mass-loss rate, kinetic power and momentum rate of the outflow as a function of the projected distance from the nucleus and the dynamical time-scale. These trends reveal multiple outflow events during the past 100 Myr, although the bulk of the mass, energy and momentum appear to have been released more recently, within the past ~20 Myr. Surprisingly, we discover that also the quiescent gas at systemic velocity is extremely extended. More specifically, we find that, while 30% of the [CII] within v\in(-200, 200) km/s traces a compact component that is not resolved by our observations, 70% of the [CII] emission in this velocity range is extended, with a projected FWHM size of 17.4+-1.4 kpc. We detect FIR continuum emission associated with both the compact and the extended [CII] components, although the extended FIR emission has a FWHM of 11+-3 kpc, thus smaller than the extended [CII] source. Overall, our results indicate that the cold gas traced by [CII] is distributed up to r~30 kpc. A large fraction of extended [CII] is likely associated with star formation on large scales, but the [CII] source extends well beyond the FIR continuum.Comment: Accepted for publication in A&A, 21 pages, 18 figures, 3 tables (v2: accepted version, discussion expanded in Sect. 3, 4 and in the Appendices, minor changes elsewhere