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

Orbits of Exceptional Groups, Duality and BPS States in String Theory

We give an invariant classification of orbits of the fundamental representations of exceptional groups $E_{7(7)}$ and $E_{6(6)}$ which classify BPS states in string and M theories toroidally compactified to d=4 and d=5. The exceptional Jordan algebra and the exceptional Freudenthal triple system and their cubic and quartic invariants play a major role in this classification. The cubic and quartic invariants correspond to the black hole entropy in d=5 and d=4, respectively. The classification of BPS states preserving different numbers of supersymmetries is in close parallel to the classification of the little groups and the orbits of timelike, lightlike and space-like vectors in Minkowski space. The orbits of BPS black holes in N=2 Maxwell-Einstein supergravity theories in d=4 and d=5 with symmetric space geometries are also classified including the exceptional N=2 theory that has $E_{7(-25)}$ and $E_{6(-26)}$ as its symmety in the respective dimensions.Comment: New references and two tables added, a new section on the orbits of N=2 Maxwell-Einstein supergravity theories in d=4 and d=5 included and some minor changes were made in other sections. 17 pages. Latex fil

Brane-anti-brane Democracy

We suggest a duality invariant formula for the entropy and temperature of non-extreme black holes in supersymmetric string theory. The entropy is given in terms of the duality invariant parameter of the deviation from extremality and 56 SU(8) covariant central charges. It interpolates between the entropies of Schwarzschild solution and extremal solutions with various amount of unbroken supersymmetries and therefore serves for classification of black holes in supersymmetric string theories. We introduce the second auxiliary 56 via E(7) symmetric constraint. The symmetric and antisymmetric combinations of these two multiplets are related via moduli to the corresponding two fundamental representations of E(7): brane and anti-brane "numbers." Using the CPT as well as C symmetry of the entropy formula and duality one can explain the mysterious simplicity of the non-extreme black hole area formula in terms of branes and anti-branes.Comment: LaTeX, 12 pages, no figure

On N=8 attractors

We derive and solve the black hole attractor conditions of N=8 supergravity by finding the critical points of the corresponding black hole potential. This is achieved by a simple generalization of the symplectic structure of the special geometry to all extended supergravities with $N>2$. There are two solutions for regular black holes, one for 1/8 BPS ones and one for the non-BPS. We discuss the solutions of the moduli at the horizon for BPS attractors using N=2 language. An interpretation of some of these results in N=2 STU black hole context helps to clarify the general features of the black hole attractors.Comment: 15 page

Effects of dark matter annihilation on the first stars

We study the evolution of the first stars in the universe (Population III) from the early pre-Main Sequence until the end of helium burning in the presence of WIMP dark matter annihilation inside the stellar structure. The two different mechanisms that can provide this energy source are the contemporary contraction of baryons and dark matter, and the capture of WIMPs by scattering off the gas with subsequent accumulation inside the star. We find that the first mechanism can generate an equilibrium phase, previously known as a "dark star", which is transient and present in the very early stages of pre-MS evolution. The mechanism of scattering and capture acts later, and can support the star virtually forever, depending on environmental characteristic of the dark matter halo and on the specific WIMP model.Comment: Proceedings of the IAU Symposium 255, "Low-Metallicity Star Formation: From the First Stars to Dwarf Galaxies"; L.K. Hunt, S. Madden and R. Schneider ed

Duality Symmetries in N=2 Heterotic Superstring

We review the derivation and the basic properties of the perturbative prepotential in N=2 compactifications of the heterotic superstring. We discuss the structure of the perturbative monodromy group and the embedding of rigidly supersymmetric monodromies associated with enhanced gauge groups, at both perturbative and non-perturbative level.Comment: Based on talks presented at several conferences. 12 pages, LaTe

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

Black Hole Superpartners and Fixed Scalars

Some bosonic solutions of supergravities admit Killing spinors of unbroken supersymmetry. The anti-Killing spinors of broken supersymmetry can be used to generate the superpartners of stringy black holes. This has a consequent feedback on the metric and the graviphoton. We have found however that the fixed scalars for the black hole superpartners remain the same as for the original black holes. Possible phenomenological implications of this result are discussed.Comment: 6 pages, Late