Generalized dimensional reduction of supergravity with eight supercharges

We describe some recent investigation about the structure of generic D=4,5 theories obtained by generalized dimensional reduction of D=5,6 theories with eight supercharges. We relate the Scherk-Schwarz reduction to a special class of N=2 no-scale gauged supergravities.Comment: Contribution to the proceedings of ``NathFest'' at PASCOS conference, Northeastern University, Boston, Ma, August 200

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

Non-BPS Attractors in 5d and 6d Extended Supergravity

We connect the attractor equations of a certain class of N=2, d=5 supergravities with their (1,0), d=6 counterparts, by relating the moduli space of non-BPS d=5 black hole/black string attractors to the moduli space of extremal dyonic black string d=6 non-BPS attractors. For d = 5 real special symmetric spaces and for N = 4,6,8 theories, we explicitly compute the flat directions of the black object potential corresponding to vanishing eigenvalues of its Hessian matrix. In the case N = 4, we study the relation to the (2,0), d=6 theory. We finally describe the embedding of the N=2, d=5 magic models in N=8, d=5 supergravity as well as the interconnection among the corresponding charge orbits.Comment: 1+27 page

On Invariant Structures of Black Hole Charges

We study "minimal degree" complete bases of duality- and "horizontal"- invariant homogeneous polynomials in the flux representation of two-centered black hole solutions in two classes of D=4 Einstein supergravity models with symmetric vector multiplets' scalar manifolds. Both classes exhibit an SL(2,R) "horizontal" symmetry. The first class encompasses N=2 and N=4 matter-coupled theories, with semi-simple U-duality given by SL(2,R) x SO(m,n); the analysis is carried out in the so-called Calabi-Vesentini symplectic frame (exhibiting maximal manifest covariance) and until order six in the fluxes included. The second class, exhibiting a non-trivial "horizontal" stabilizer SO(2), includes N=2 minimally coupled and N=3 matter coupled theories, with U-duality given by the pseudo-unitary group U(r,s) (related to complex flux representations). Finally, we comment on the formulation of special Kaehler geometry in terms of "generalized" groups of type E7.Comment: 1+24 pages; 1 Table. v2 : Eqs. (1.2) and (1.3) added; Eq. (2.87) change

On the [CII]-SFR relation in high redshift galaxies

After two ALMA observing cycles, only a handful of [CII] $158\,\mu m$ emission line searches in z>6 galaxies have reported a positive detection, questioning the applicability of the local [CII]-SFR relation to high-z systems. To investigate this issue we use the Vallini et al. 2013 (V13) model, based on high-resolution, radiative transfer cosmological simulations to predict the [CII] emission from the interstellar medium of a z~7 (halo mass $M_h=1.17\times10^{11}M_{\odot}$) galaxy. We improve the V13 model by including (a) a physically-motivated metallicity (Z) distribution of the gas, (b) the contribution of Photo-Dissociation Regions (PDRs), (c) the effects of Cosmic Microwave Background on the [CII] line luminosity. We study the relative contribution of diffuse neutral gas to the total [CII] emission ($F _{diff}/F_{tot}$) for different SFR and Z values. We find that the [CII] emission arises predominantly from PDRs: regardless of the galaxy properties, $F _{diff}/F_{tot}\leq 10$% since, at these early epochs, the CMB temperature approaches the spin temperature of the [CII] transition in the cold neutral medium ($T_{CMB}\sim T_s^{CNM}\sim 20$ K). Our model predicts a high-z [CII]-SFR relation consistent with observations of local dwarf galaxies ($0.02<Z/Z_{\odot}<0.5$). The [CII] deficit suggested by actual data ($L_{CII}<2.0\times 10^7 L_{\odot}$ in BDF3299 at z~7.1) if confirmed by deeper ALMA observations, can be ascribed to negative stellar feedback disrupting molecular clouds around star formation sites. The deviation from the local [CII]-SFR would then imply a modified Kennicutt-Schmidt relation in z>6 galaxies. Alternatively/in addition, the deficit might be explained by low gas metallicities ($Z<0.1 Z_{\odot}$).Comment: 9 pages, 6 figures, replaced with the version accepted for pubblication in Ap

On the Super Higgs Effect in Extended Supergravity

We consider the reduction of supersymmetry in N-extended four dimensional supergravity via the super Higgs mechanism in theories without cosmological constant. We provide an analysis largely based on the properties of long and short multiplets of Poincare' supersymmetry. Examples of the super Higgs phenomenon are realized in spontaneously broken N=8 supergravity through the Scherk-Schwarz mechanism and in superstring compactification in presence of brane fluxes. In many models the massive vectors count the difference in number of the translation isometries of the scalar sigma-model geometries in the broken and unbroken phase.Comment: Version to appear on Nuclear Physics

Freudenthal Dual Lagrangians

The global U-dualities of extended supergravity have played a central role in differentiating the distinct classes of extremal black hole solutions. When the U-duality group satisfies certain algebraic conditions, as is the case for a broad class of supergravities, the extremal black holes enjoy a further symmetry known as Freudenthal duality (F-duality), which although distinct from U-duality preserves the Bekenstein-Hawking entropy. Here it is shown that, by adopting the doubled Lagrangian formalism, F-duality, defined on the doubled field strengths, is not only a symmetry of the black hole solutions, but also of the equations of motion themselves. A further role for F-duality is introduced in the context of world-sheet actions. The Nambu-Goto world-sheet action in any (t, s) signature spacetime can be written in terms of the F-dual. The corresponding field equations and Bianchi identities are then related by F-duality allowing for an F-dual formulation of Gaillard-Zumino duality on the world-sheet. An equivalent polynomial "Polyakov- type" action is introduced using the so-called black hole potential. Such a construction allows for actions invariant under all groups of type E7, including E7 itself, although in this case the stringy interpretation is less clear.Comment: 1+16 pages, 1 Table, updated to match published versio

Matrix Norms, BPS Bounds and Marginal Stability in N=8 Supergravity

We study the conditions of marginal stability for two-center extremal black holes in N-extended supergravity in four dimensions, with particular emphasis on the N=8 case. This is achieved by exploiting triangle inequalities satisfied by matrix norms. Using different norms and relative bounds among them, we establish the existence of marginal stability and split attractor flows both for BPS and some non-BPS solutions. Our results are in agreement with previous analysis based on explicit construction of multi-center solutions.Comment: 1+15 pages; v2: some new formulas added and misprints corrected; v3: typos fixed, various refinements, Sec. 2.4 rewritten; to appear on JHE

Contour spectrograms for POGO analysis

Contour spectrograms for POGO analysis in Saturn S-2 and S-4b stage

Two-Centered Magical Charge Orbits

We determine the two-centered generic charge orbits of magical N = 2 and maximal N = 8 supergravity theories in four dimensions. These orbits are classified by seven U-duality invariant polynomials, which group together into four invariants under the horizontal symmetry group SL(2,R). These latter are expected to disentangle different physical properties of the two-centered black-hole system. The invariant with the lowest degree in charges is the symplectic product (Q1,Q2), known to control the mutual non-locality of the two centers.Comment: 1+17 pages, 1 Table; v2: Eq. (3.23) corrected; v3: various refinements in text and formulae, caption of Table 1 expanded, Footnote and Refs. added. To appear on JHE