Four curious supergravities

We consider four supergravities with 16+16, 32+32, 64+64, 128+128 degrees of freedom displaying some curious properties: (1) They exhibit minimal supersymmetry (N=1, 2, 2, 1) but maximal rank (r=7, 6, 4, 0) of the scalar coset in D=4, 5, 7, 11. (2) They couple naturally to supermembranes and admit these membranes as solutions. (3) Although the D=4, 5, 7 supergravities follow from truncating the maximally supersymmetric ones, there nevertheless exist M-theory compactifications with G2, SU(3), SU(2) holonomy having these supergravities as their massless sectors. (4) They reduce to N=1, 2, 4, 8 theories all with maximum rank 7 in D=4 which (5) correspond to 0, 1, 3, 7 lines of the Fano plane and hence admit a division algebra (R,C,H,O) interpretation consistent with the black-hole/qubit correspondence, (6) are generalized self-mirror and hence (7) have vanishing on-shell trace anomaly.Comment: 16 pages late

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

Common business and housing market cycles in the Euro area from a multivariate decomposition.

The 2007 sub-prime crisis in the United States, prolonged by a severe economic recession spread over many countries around the world, has led many economic researchers to focus on the recent fluctuations in housing prices and their relationships with macroeconomics and monetary policies. The existence of common housing cycles among the countries of the euro zone could lead the European Central Bank to integrate more specifically the evolution of such asset prices in its assessment. In this paper, we implement a multivariate unobserved component model on housing market variables in order to assess the common euro area housing cycle and to evaluate its relationship with the economic cycle. Among the general class of multivariate unobserved component models, we implement the band-pass filter based on the trend plus cycle decomposition model and we allow the existence of two cycles of different periods. The dataset consists of gross domestic product and real house prices series for four main euro area countries (Germany, France, Italy and Spain). Empirical results show a strong relationship for business cycles in France, Italy and Spain. Moreover, French and Spanish house prices cycles appear to be strongly related, while the German one possesses its own dynamics. Finally, we find that GDP and house prices cycles are related in the medium-term for fluctuations between 4 and 8 years, while the housing market contributes to the long-term economic growth only in Spain and Germany.House prices, Business cycles, Euro area, Unobserved components model.

On Black Attractors in 8D and Heterotic/Type IIA Duality

Motivated by the study of black attractors in 8D supergravity with 16 supersymmetries, we use the field theory approach and 8D supersymmetry with non trivial central charges to shed light on the exact duality between heterotic string on T^2 and type IIA on real connected and compact surfaces {\Sigma}2. We investigate the two constraints that should be obeyed by {\Sigma}2 and give their solutions in terms of intersecting 2-cycles as well their classification using Dynkin diagrams of affine Kac-Moody algebras. It is shown as well that the moduli space of these dual theories is given by SO(1,1)x((SO(2,r+2))/(SO(2)xSO(r+2))) where r stands for the rank of the gauge symmetry G_{r} of the 10D heterotic string on T^2. The remarkable cases r=-2,-1,0 as well as other features are also investigated.Comment: LaTex, 18 pages, 2 figures, To appear in JHE

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

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

Picard-Fuchs Equations and Special Geometry

We investigate the system of holomorphic differential identities implied by special K\"ahlerian geometry of four-dimensional N=2 supergravity. For superstring compactifications on \cy threefolds these identities are equivalent to the Picard-Fuchs equations of algebraic geometry that are obeyed by the periods of the holomorphic three-form. For one variable they reduce to linear fourth-order equations which are characterized by classical $W$-generators; we find that the instanton corrections to the Yukawa couplings are directly related to the non-vanishing of $w_4$. We also show that the symplectic structure of special geometry can be related to the fact that the Yukawa couplings can be written as triple derivatives of some holomorphic function $F$. Moreover, we give the precise relationship of the Yukawa couplings of special geometry with three-point functions in topological field theory.Comment: 43 page

Supersymmetric Sum Rules for Electromagnetic Multipoles

We derive model independent, non-perturbative supersymmetric sum rules for the magnetic and electric multipole moments of any theory with N=1 supersymmetry. We find that in any irreducible N=1 supermultiplet the diagonal matrix elements of the l-multipole moments are completely fixed in terms of their off-diagonal matrix elements and the diagonal (l-1)-multipole moments.Comment: 10 pages, plain Te