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

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

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

Maurer-Cartan Equations and Black Hole Superpotentials in N =8 Supergravity

We retrieve the non-BPS extremal black hole superpotential of N=8, d=4 supergravity by using the Maurer-Cartan equations of the symmetric space E_7(7)/SU(8). This superpotential was recently obtained with different 3- and 4-dimensional techniques. The present derivation is independent on the reduction to d=3.Comment: 1+22 page

(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