The structure of N=3 multiplets in AdS_4 and the complete Osp(3|4) X SU(3) spectrum of M-theory on AdS_4 X N^{010}

In this paper, relying on previous results of one of us on harmonic analysis, we derive the complete spectrum of Osp(3|4) X SU(3) multiplets that one obtains compactifying D=11 supergravity on the unique homogeneous space N^{0,1,0} that has a tri-sasakian structure, namely leads to N=3 supersymmetry both in the four-dimensional bulk and on the three-dimensional boundary. As in previously analyzed cases the knowledge of the Kaluza Klein spectrum, together with general information on the geometric structure of the compact manifold is an essential ingredient to guess and construct the corresponding superconformal field theory. This is work in progress. As a bonus of our analysis we derive and present the explicit structure of all unitary irreducible representations of the superalgebra Osp(3|4) with maximal spin content s_{max}>=2.Comment: Latex2e, 13+1 page

R-Symmetry, twisted N=2 Theory and the Role of the Dilaton

We discuss R-symmetry in locally supersymmetric $N=2$ gauge theories coupled to hypermultiplets, which can be viewed as effective theories of heterotic string models. In this type of supergravities a suitable R-symmetry exists and can be used to topologically twist the theory. The vector multiplet of the dilaton-axion field has a different R-charge assignment with respect to the other vector multiplets.Comment: Proceedings of ``Susy95'', Palaiseaux, Ecole Polytechnique, May 95 LaTex, 8 pg

On the supergravity formulation of mirror symmetry in generalized Calabi-Yau manifolds

We derive the complete supergravity description of the N=2 scalar potential which realizes a generic flux-compactification on a Calabi-Yau manifold (generalized geometry). The effective potential V_{eff}=V_{(\partial_Z V=0)}, obtained by integrating out the massive axionic fields of the special quaternionic manifold, is manifestly mirror symmetric, i.e. invariant with respect to {\rm Sp}(2 h_2+2)\times {\rm Sp}(2 h_1+2) and their exchange, being h_1, h_2 the complex dimensions of the underlying special geometries. {\Scr V}_{eff} has a manifestly N=1 form in terms of a mirror symmetric superpotential W$ proposed, some time ago, by Berglund and Mayr.Comment: 14 pages, LaTeX sourc

N=1 domain wall solutions of massive type II supergravity and the issue of mirror symmetry

We report on Domain Wall solution of Calabi-Yau compactifications with general fluxes and their application to the study of mirror symmetry in generalized backgrounds. We address, in particular, to the issue of magnetic NSNS fluxes. We show that the Domain Wall gradient flow equations can be interpreted as a set of generalized Hitchin's flow equations of a manifold with SU(3)x SU(3) structure fibered along the direction transverse to the Domain wall.Comment: To appear in the proceedings of 2nd RTN Network Workshop and Midterm Meeting: Constituents, Fundamental Forces and Symmetries of the Universe, Naples, Italy, 9-13 Oct 200

Poincare' dual of D=4 N=2 Supergravity with Tensor Multiplets

We study, in an arbitrary even number D of dimensions, the duality between massive D/2 tensors coupled to vectors, with masses given by an arbitrary number of ``electric'' and ``magnetic'' charges, and (D/2-1) massive tensors. We develop a formalism to dualize the Lagrangian of D=4, N=2 supergravity coupled to tensor and vector multiplets, and show that, after the dualization, it is equivalent to a standard D=4, N=2 gauged supergravity in which the Special Geometry quantities have been acted on by a suitable symplectic rotation.Comment: 15 pages, JHEP3 class, v2 typos corrected, references adde

Dyonic Masses from Conformal Field Strengths in D even Dimensions

We show that D/2--form gauge fields in D even dimensions can get a mass with both electric and magnetic contributions when coupled to conformal field--strengths whose gauge potentials is are \frac {D-2}{2}- forms. Denoting by e^I_\L and m^{I\L} the electric and magnetic couplings, gauge invariance requires: e^I_\L m^{J\L}\mp e^J_\L m^{I\L}=0, where I,\L= 1... m denote the species of gauge potentials of degree D/2 and gauge fields of degree D/2-1, respectively. The minus and plus signs refer to the two different cases D=4n and D=4n+2 respectively and the given constraints are respectively {\rm {Sp}}(2m) and {\rm {O}}(m,m) invariant. For the simplest examples, (I,\L=1 for D=4n and I,\L=1,2 for D=4n+2) both the e,m quantum numbers contribute to the mass \m=\sqrt {e^2 +m^2} . This phenomenon generalizes to $D$ even dimensions the coupling of massive antisymmetric tensors which appear in D=4 supergravity Lagrangians which derive from flux compactifications in higher dimensions. For D=4 we give the supersymmetric generalization of such couplings using N=1 superspace.Comment: 11 pages, LaTeX source, typos corrected. Version to appear on Phys.Lett.

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

Twisted tori and fluxes: a no go theorem for Lie groups of weak G_2 holonomy

In this paper we prove the theorem that there exists no 7--dimensional Lie group manifold G of weak G2 holonomy. We actually prove a stronger statement, namely that there exists no 7--dimensional Lie group with negative definite Ricci tensor Ric_{IJ}. This result rules out (supersymmetric and non--supersymmetric) Freund--Rubin solutions of M--theory of the form AdS_4\times G and compactifications with non--trivial 4--form fluxes of Englert type on an internal group manifold G. A particular class of such backgrounds which, by our arguments are excluded as bulk supergravity compactifications corresponds to the so called compactifications on twisted--tori, for which G has structure constants $\tau^K{}_{IJ}$ with vanishing trace $\tau^J{}_{IJ}=0$. On the other hand our result does not have bearing on warped compactifications of M--theory to four dimensions and/or to compactifications in the presence of localized sources (D--branes, orientifold planes and so forth). Henceforth our result singles out the latter compactifications as the preferred hunting grounds that need to be more systematically explored in relation with all compactification features involving twisted tori.Comment: 38 pages, tar file containing LaTeX source and youngtab.st

String Quantum Symmetries From Picard-Fuchs Equations And Their Monodromy

Local and global properties of the moduli space of Calabi--Yau type compactifications determine the low energy parameters of the string effective action. We show that the moduli space geometry is entirely encoded in the Picard--Fuchs equations for the periods of the Calabi--Yau $H^{(3)}$--cohomology.Comment: 33 pages, plain TeX, CERN-TH.6777/93,POLFIS-TH.24/9