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

Short representations of SU(2,2/N) and harmonic superspace analyticity

We consider the harmonic superspaces associated to SU(2,2/N) superconformal algebras. For arbitrary N, we show that massless representations, other than the chiral ones, correspond to [N/2] ``elementary'' ultrashort analytic superfields whose first component is a scalar in the k antisymmetric irrep of SU(N) (k=1... [N/2]) with top spin $J_{\rm\scriptsize top}= (N/2-k/2,0)$. For N=2n we analyze UIR's obtained by tensoring the self-conjugate ultrashort multiplet $J_{\rm\scriptsize top}$= (n/2,0) and show that N-1 different basic products give rise to all possible UIR's with residual shortening.Comment: references adde

Properties of the Lyman Alpha Clouds from non-equilibrium Photoionization Models

We investigate the thermal and ionization history of Lyman alpha clouds photoionized by a time--dependent UV background, including non equilibrium effects. The results show that it is possible to obtain temperatures as low as T~15000 K (or, equivalently, Doppler parameters b~15 km/s) at z=3 for cloud total densities n~10^-4 cm^-3, if (i) the reionization epoch occurred at z_i~10, and (ii) the UV background has a factor 70-100 decrease at the HeII edge. A trend towards smaller b with increasing redshift is present in the redshift interval z=1-5. Higher densities lead to higher values of b and smaller hydrogen correction factors, n_{HII}/n_{HI}. The correction factors for helium are also given. For a hydrogen column density N_{HI}=3 10^{14} cm^{-2}, cloud sizes are larger than 100 kpc, consistent with recent observations of quasar pairs. Pressure confined models, instead, yield implausibly low cloud densities at low redshift, and too small sizes at intermediate redshift. The implications of the model are confronted with the available observational data.Comment: 6 pages, 4 figures, mnras in pres

(2,0) Superconformal OPEs in D=6, Selection Rules and Non-renormalization Theorems

We analyse the OPE of any two 1/2 BPS operators of (2,0) SCFT$_6$ by constructing all possible three-point functions that they can form with another, in general long operator. Such three-point functions are uniquely determined by superconformal symmetry. Selection rules are derived, which allow us to infer ``non-renormalization theorems'' for an abstract superconformal field theory. The latter is supposedly related to the strong-coupling dynamics of $N_c$ coincident M5 branes, dual, in the large-$N_c$ limit, to the bulk M-theory compactified on AdS$_7 \times$S$_4$. An interpretation of extremal and next-to-extremal correlators in terms of exchange of operators with protected conformal dimension is given.Comment: some details correcte

Non-anticommutative chiral singlet deformation of N=(1,1) gauge theory

We study the SO(4)x SU(2) invariant Q-deformation of Euclidean N=(1,1) gauge theories in the harmonic superspace formulation. This deformation preserves chirality and Grassmann harmonic analyticity but breaks N=(1,1) to N=(1,0) supersymmetry. The action of the deformed gauge theory is an integral over the chiral superspace, and only the purely chiral part of the covariant superfield strength contributes to it. We give the component form of the N=(1,0) supersymmetric action for the gauge groups U(1) and U(n>1). In the U(1) and U(2) cases, we find the explicit nonlinear field redefinition (Seiberg-Witten map) relating the deformed N=(1,1) gauge multiplet to the undeformed one. This map exists in the general U(n) case as well, and we use this fact to argue that the deformed U(n) gauge theory can be nonlinearly reduced to a theory with the gauge group SU(n).Comment: 1+25 pages; v2: corrected eqs.(2.7),(3.12),(4.31-33) and typos; v3: corrected eqs.(3.29),(4.7),(A.5),(A.21), ref. added, published versio

The Role of Stellar Feedback and Dark Matter in the Evolution of Dwarf Galaxies

Supernova and multiple supernova events regulate several structural properties of dwarf galaxies. In particular, they govern the metal enrichment and the energy budget of the ISM; they might induce partial (blowout) or total (blowaway) gas removal from the galaxy; the morphology of the galactic gaseous body. Significant amounts of dark matter may play an equally important role: the dark matter gravitational potential tends to concentrate baryons towards the center, thus enhancing both the star formation rate and metal production. Also, the dynamical properties of the ISM, and the occurrence of a blowout or blowaway are shown to be determined by the dark matter content. We present detailed analytical/numerical models describing the evolution of dwarf Irregular galaxies including the above and other effects. The main results are: (i) dwarfs with total masses M\simlt 5\times 10^6 M_\odot are blown away; those with gas masses up to $\simeq 10^9 M_\odot$ lose mass in an outflow; (ii) metallicities are found to correlate tightly with dark matter content and are consistent with a range of dark-to-visible mass ratios $\phi\approx 0-30$ with about 65% of the dwarfs in the sample having $\phi\approx 0-10$; (iii) we predict a lower limit to the oxygen abundance in dIs of $12+log(O/H)\approx 7.2$; (iv) outflows are not particularly important for the metallicity evolution of dwarf galaxies and certainly less than star formation for gas consumption; however, dwarfs with gas masses few $\times 10^8 M_\odot$ are shown to be the major pollutants of the IGM; (v) the ISM HI velocity dispersion correlates with metallicity and, indepentently of dark matter, scales as $Z^{3.5}$. (Abridged)Comment: 56 pages, aasms4.sty, LaTeX, 12 figures. MNRAS, submitte

Where are the missing cosmic metals ?

The majority of the heavy elements produced by stars 2 billion years after the Big Bang (redshift z~3) are presently undetected at those epochs. We propose a solution to this cosmic `missing metals' problem in which such elements are stored in gaseous halos produced by supernova explosions around star-forming galaxies. By using data from the ESO/VLT Large Program, we find that:(i) only 5%-9% of the produced metals reside in the cold phase, the rest being found in the hot (log T=5.8-6.4) phase; (ii) 1%-6% (3%-30%) of the observed CIV (OVI) is in the hot phase. We conclude that at z~3 more than 90% of the metals produced during the star forming history can be placed in a hot phase of the IGM, without violating any observational constraint. The observed galaxy mass-metallicity relation, and the intergalactic medium and intracluster medium metallicity evolution are also naturally explained by this hypothesis.Comment: 9 pages, 2 figures, ApJ Letters, in pres

Backreaction I: The Torus

We use wrapped D-brane probes to measure position dependent perturbations of compactification moduli. Due to the backreaction of the D-branes on the local geometry, we suspect that measuring the fluctuations of one modulus to high precision will generically affect the others. These considerations lead us to conjecture a novel uncertainty principle on the Calabi-Yau moduli space. We begin our investigation with a gedanken experiment on a torus.Comment: 15 pages, 5 eps figures, clarifying comments adde

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