On the underlying E11 symmetry of the D=11 Free Differential Algebra

We study the reduction of the Free Differential Algebra (FDA) of D=11 supergravity to an ordinary algebra. We show that in flat background and with vanishing three-form field strength, the corresponding minimal FDA can be reduced to an Inonu-Wigner contraction of Sezgin's M-Algebra. We also prove that in flat background but with a non trivial three-form field strength, the bosonic FDA can be reduced to the lowest levels of E11. This result suggests that the E11 symmetries, which act on perturbative states as well, are already encoded in the D=11 FDA and are made explicit when the theory is formulated on a enlarged group manifold.Comment: 25 pages, LaTeX, typos corrected, final version published in JHE

On the construction of variant supergravities in D=11, D=10

We construct with a geometric procedure the supersymmetry transformation laws and Lagrangian for all the ``variant'' D=11 and D=10 Type IIA supergravities. We identify into our classification the D=11 and D=10 Type IIA ``variant'' theories first introduced by Hull performing T-duality transformation on both spacelike and timelike circles. We find in addition a set of D=10 Type IIA ``variant'' supergravities that can not be obtained trivially from eleven dimensions compactifying on a circle.Comment: 21 pages, Late

Domain Wall/Cosmology correspondence in (AdS/dS)_6 x S^4 geometries

We investigate the ten dimensional origin of six dimensional F_4 variant supergravity with supersymmetric de Sitter background. We address first the issue of spontaneous compactification, showing that it consists of a warped compactification on a four sphere of a variant massive type IIA supergravity. Moreover we illustrate how the known D4-D8 brane solution, whose near horizon geometry yields AdS_6 x S^4, is accordingly modified to a system including Euclidean branes. Finally, we discuss the relation between this latter solution and the D4-D8 brane system, showing how it represents a generalisation of the DW/Cosmology correspondence.Comment: 11 pages, LaTe

D=6, N=2, F(4)-Supergravity with supersymmetric de Sitter Background

We show that there exists a supersymmetric de Sitter background for the D=6, N=2, F(4) supergravity preserving the compact R-symmetry and gauging with respect to the conventional Anti de Sitter version of the theory. We construct the gauged matter coupled F(4) de Sitter supergravity explicitly and show that it contains ghosts in the vector sector.Comment: 19 pages, Late

N=4 supergravity for Type IIB on T^6/Z_2 in presence of fluxes

We report on the construction of four dimensional gauged supergravity models that can be interpreted as type IIB orientifold compactification in presence of 3-form fluxes and D3--branes. We mainly address our attention to the symplectic embedding of the U-duality group of the theory and the consequent choice of the gauge group, whose four dimensional killing vectors are the remnant of the ten dimensional fluxes. We briefly discuss the structure of the scalar potential arising from the gauging and the properties of the killing vectors in order to preserve some amount of supersymmetry.Comment: LaTeX, iopart class, 9 pages, Contribution to the proceedings of the workshop of the RTN Network "The quantum structure of space-time and the geometric nature of fundamental interactions",Copenhagen, September 2003 2nd version, references adde

N=1 domain wall solutions of massive type II supergravity as generalized geometries

We study N=1 domain wall solutions of type IIB supergravity compactified on a Calabi-Yau manifold in the presence of RR and NS electric and magnetic fluxes. We show that the dynamics of the scalar fields along the direction transverse to the domain wall is described by gradient flow equations controlled by a superpotential W. We then provide a geometrical interpretation of the gradient flow equations in terms of the mirror symmetric compactification of type IIA. They correspond to a set of generalized Hitchin flow equations of a manifold with SU(3)xSU(3)structure which is fibered over the direction transverse to the domain wall.Comment: 28 pages, LaTe

N=4 Supergravity Lagrangian for Type IIB Orientifold on T^6/Z_2 in Presence of Fluxes and D3-Branes

We derive the Lagrangian and the transformation laws of N=4 gauged supergravity coupled to matter multiplets whose sigma-model of the scalars is SU(1,1)/U(1)x SO(6,6+n)/SO(6)xSO(6+n) and which corresponds to the effective Lagrangian of the Type IIB string compactified on the T^6/Z_2 orientifold with fluxes turned on and in presence of n D3-branes. The gauge group is T^12 x G where G is the gauge group on the brane and T^12 is the gauge group on the bulk corresponding to the gauged translations of the R-R scalars coming from the R-R four--form. The N=4 bulk sector of this theory can be obtained as a truncation of the Scherk-Schwarz spontaneously broken N=8 supergravity. Consequently the full bulk spectrum satisfies quadratic and quartic mass sum rules, identical to those encountered in Scherk-Schwarz reduction gauging a flat group. This theory gives rise to a no scale supergravity extended with partial super-Higgs mechanism.Comment: 49 pages, LaTex, 2 figures. Misprints corrected, more comments adde

Domain wall flow equations and SU(3)xSU(3) structure compactifications

We study supersymmetric domain wall solutions in four dimensions arising from the compactification of type II supergravity on a SU(3)xSU(3) structure manifold. Using a pure spinor approach, we show that the supersymmetry variations can be reinterpreted as a generalisation of the Hitchin flow equations and describe the embedding of a SU(3)xSU(3) structure manifold into a G_2xG_2 structure manifold. We find a precise agreement between the four- and ten-dimensional supergravity results. The flow equations derived here should have applications in constructing the gravity duals of Chern-Simons-matter conformal field theories.Comment: 54 pages. v2: references added and acknowledgments updated. v3: published versio

All the timelike supersymmetric solutions of all ungauged d=4 supergravities

We determine the form of all timelike supersymmetric solutions of all N greater or equal than 2, d=4 ungauged supergravities, for N less or equal than 4 coupled to vector supermultiplets, using the $Usp(n+1,n+1)-symmetric formulation of Andrianopoli, D'Auria and Ferrara and the spinor-bilinears method, while preserving the global symmetries of the theories all the way. As previously conjectured in the literature, the supersymmetric solutions are always associated to a truncation to an N=2 theory that may include hypermultiplets, although fields which are eliminated in the truncations can have non-trivial values, as is required by the preservation of the global symmetry of the theories. The solutions are determined by a number of independent functions, harmonic in transverse space, which is twice the number of vector fields of the theory (n+1). The transverse space is flat if an only if the would-be hyperscalars of the associated N=2 truncation are trivial.Comment: v3: Some changes in the introduction. Version to be published in JHE