Gauge Charges from Supergravity

Some recent results in the study of four dimensional supergravity flux compactifications are reviewed, discussing in particular the role of torsion on the compactification manifold in generating gauge charges for the effective four dimensional theories.Comment: Contribution to the 43rd International School of Subnuclear Physics, Erice, Sicily, Italy, Aug. 200

U(N) Gauged N=2 Supergravity and Partial Breaking of Local N=2 Supersymmetry

We study a minimal model of U(N) gauged N=2 supergravity with one hypermultiplet parametrizing SO(4,1)/SO(4) quaternionic manifold. Local N=2 supersymmetry is known to be spontaneously broken to N=1 in the Higgs phase of U(1)_{graviphoton} \times U(1). Several properties are obtained of this model in the vacuum of unbroken SU(N) gauge group. In particular, we derive mass spectrum analogous to the rigid counterpart and put the entire effective potential on this vacuum in the standard superpotential form of N=1 supergravity.Comment: 22 pages, a version to appear Int. J. Mod. Phys.

Supergravities in diverse dimensions and their central extension

In this lecture moduli dependent charges for p-extended objects are analyzed for generic N-extended supergravities in dimensions 4 \leq D <10. Differential relations and sum rules among the charges are derived.Comment: 10 pages, LaTeX; Talk given at the WorkShop on Gauge Theories, Applied Supersymmetry and Quantum Gravity, London, 5-10 July 199

Extremal Black Holes in Supergravity and the Bekenstein-Hawking Entropy

We review some results on the connection among supergravity central charges, BPS states and Bekenstein-Hawking entropy. In particular, N=2 supergravity in four dimensions is studied in detail. For higher N supergravities we just give an account of the general theory specializing the discussion to the N=8 case when one half of supersymmetry is preserved. We stress the fact that for extremal supergravity black holes the entropy formula is topological, that is the entropy turns out to be a moduli independent quantity and can be written in terms of invariants of the duality group of the supergravity theory.Comment: LaTeX, 65 pages. Contribution to the journal ``Entropy'', ISSN 1099-430

More on the Hidden Symmetries of 11D Supergravity

In this paper we clarify the relations occurring among the osp(1|32) algebra, the M-algebra and the hidden superalgebra underlying the Free Differential Algebra of D=11 supergravity (to which we will refer as DF-algebra) that was introduced in the literature by D'Auria and Fr\'e in 1981 and is actually a (Lorentz valued) central extension of the M-algebra including a nilpotent spinor generator, Q'. We focus in particular on the 4-form cohomology in 11D superspace of the supergravity theory, strictly related to the presence in the theory of a 3-form $A^{(3)}$. Once formulated in terms of its hidden superalgebra of 1-forms, we find that $A^{(3)}$ can be decomposed into the sum of two parts having different group-theoretical meaning: One of them allows to reproduce the FDA of the 11D Supergravity due to non-trivial contributions to the 4-form cohomology in superspace, while the second one does not contribute to the 4-form cohomology, being a closed 3-form in the vacuum, defining however a one parameter family of trilinear forms invariant under a symmetry algebra related to osp(1|32) by redefining the spin connection and adding a new Maurer-Cartan equation. We further discuss about the crucial role played by the 1-form spinor $\eta$ (dual to the nilpotent generator Q') for the 4-form cohomology of the eleven dimensional theory on superspace.Comment: Title and abstract changed to better represent the content, some points clarified, mainly in Section 2 and in the concluding section, references added. Version accepted for publication on Physics Letters

Central Extension of Extended Supergravities in Diverse Dimensions

We generalize central-charge relations and differential identities of N=2 Special Geometry to N extended supergravity in any dimension 4 \leq D <10, and p-extended objects. We study the extremization of the ADM mass per unit of p-volume of BPS extended objects. Runaway solutions for a ``dilaton'' degree of freedom leading to a vanishing result are interpreted as BPS extremal states having vanishing Bekenstein-Hawking Entropy.Comment: 13 pages, LaTeX, no figures. This is the last version which will appear in International Journal of Modern Physics

Consistent reduction of N=2 -> N=1 four dimensional supergravity coupled to matter

We analyze the constraints which follow both on the geometry and on the gauge sector for a consistent supergravity reduction of a general matter-coupled N=2 supergravity theory in four dimensions. These constraints can be derived in an elegant way by looking at the fermionic sector of the theory.Comment: LaTeX, 16 page

U-Duality and Central Charges in Various Dimensions Revisited

A geometric formulation which describes extended supergravities in any dimension in presence of electric and magnetic sources is presented. In this framework the underlying duality symmetries of the theories are manifest. Particular emphasis is given to the construction of central and matter charges and to the symplectic structure of all D=4, N-extended theories. The latter may be traced back to the existence, for N>2, of a flat symplectic bundle which is the N>2 generalization of N=2 Special Geometry.Comment: Misprints corrected and some relations added in six dimensional non-chiral theorie

D=4, N=2 Gauged Supergravity in the Presence of Tensor Multiplets

Using superspace techniques we construct the general theory describing D=4, N=2 supergravity coupled to an arbitrary number of vector and scalar--tensor multiplets. The scalar manifold of the theory is the direct product of a special Kaehler and a reduction of a Quaternionic-Kaehler manifold. We perform the electric gauging of a subgroup of the isometries of such manifold as well as ``magnetic'' deformations of the theory discussing the consistency conditions arising in this process. The resulting scalar potential is the sum of a symplectic invariant part (which in some instances can be recast into the standard form of the gauged N =2 theory) and of a non--invariant part, both giving new deformations. We also show the relation of such theories to flux ompactifications of type II string theories.Comment: LaTeX, 26 pages. v2 Improved discussion in sect. 4 and references adde

The minimal N=4 no-scale model from generalized dimensional reduction

We consider the generalized dimensional reduction of pure ungauged N=4, D=5 supergravity, where supersymmetry is spontaneously broken to N=2 or N=0 with identically vanishing scalar potential. We explicitly construct the resulting gauged D=4 theory coupled to a single vector multiplet, which provides the minimal N=4 realization of a no-scale model. We discuss its relation with the standard classification of N=4 gaugings, extensions to non-compact twists and to higher dimensions, the N=2 theories obtained via consistent Z_2 orbifold projections and prospects for further generalizations.Comment: 1+28 pages, no figures, JHEP3 LaTeX, published versio