Supersymmetric M2-branes with Englert Fluxes and the simple group PSL(2,7)

A new class is introduced of M2-branes solutions of d=11 supergravity that include internal fluxes obeying Englert equation in 7-dimensions. A simple criterion for the existence of Killing spinors in such backgrounds is established. Englert equation is viewed as the generalization to d=7 of Beltrami equation defined in d=3 and it is trated accordingly. All 2-brane solutions of minimal d=7 supergracity can be uplifted to d=11 and have N > 4 or N = 4 supersymmetry. It is shown that the simple group PSL(2,7) is crystallographic in d=7 having an integral action on the A7 root lattice. By means of this point-group and of the T7 torus obtained quotiening R7 with the A7 root lattice we were able to construct new M2 branes with Englert fluxes and N < 4. In particular we exhibit here an N=1 solution depending on 4-parameters and admitting a large non abelian discrete symmetry, namely G21 = Z3 semidirect product with Z7 = subgroup of PSL(2,7). The dual d=3 field theories have the same symmetries and have complicated non linear interactions.Comment: 59 pages, two figures. Original Research Article. Few misprints corrected, a pair of sentences added in the aknowledgment

BPS D3-branes on smooth ALE manifolds

In this talk I review the recent construction of a new family of classical BPS solutions of type IIB supergravity describing 3-branes transverse to a 6-dimensional space with topology $\mathbb{R}^{2}\times$ALE. They are characterized by a non-trivial flux of the supergravity 2-forms through the homology 2-cycles of a generic smooth ALE manifold. These solutions have two Killing spinors and thus preserve $\mathcal{N}=2$ supersymmetry. They are expressed in terms of a quasi harmonic function $H$ (the ``warp factor''), whose properties was studied in detail in the case of the simplest ALE, namely the Eguchi-Hanson manifold. The equation for $H$ was identified as an instance of the confluent Heun equation.Comment: Talk given at the Conference "New Trends in Particle Physics", September 2001, Yalta, Ukrain

BPS Black Holes in Superegravity

In these lectures we explain the concept of supergravity p-branes and BPS black holes. Introducing an audience of general relativists to all the necessary geometry related with extended supergravity (special geometry, symplectic embeddings and the like) we describe the general properties of N=2 black holes, the structure of central charges in extended supergravity and the description of black hole entropy as an invariant of the U duality group. Then, after explaining the concept and the use of solvable Lie algebras we present the detailed construction of 1/2, 1/4 and 1/8 supersymmetry preserving black holes in the context of N=8 supergravity. The Lectures are meant to be introductory and self contained for non supersymmetry experts but at the same time fully detailed and complete on the subject.Comment: LaTeX, 132 pages, Book.sty. Lecture Notes for the SIGRAV Graduate School in Contemporary Relativity, Villa Olmo, Como First Course, April 199

Stable de Sitter Vacua from N=2 Supergravity

We find extrema of the potential of matter couplings to N=2 supergravity that define de Sitter vacua and no tachyonic modes. There are three essential ingredients in our construction: namely non-abelian non-compact gaugings, de Roo-Wagemans rotation angles, and Fayet-Iliopoulos terms.Comment: 30 pages, 1 figure; v2: Added reference, and typos corrected. Version to be published in CQ

On the Topology of the Inflaton Field in Minimal Supergravity Models

We consider global issues in minimal supergravity models where a single field inflaton potential emerges. In a particular case we reproduce the Starobinsky model and its description dual to a certain formulation of R+R^2 supergravity. For definiteness we confine our analysis to spaces at constant curvature, either vanishing or negative. Five distinct models arise, two flat models with respectively a quadratic and a quartic potential and three based on the SU(1,1)/U(1) space where its distinct isometries, elliptic, hyperbolic and parabolic are gauged. Fayet-Iliopoulos terms are introduced in a geometric way and they turn out to be a crucial ingredient in order to describe the de Sitter inflationary phase of the Starobinsky model.Comment: 31 pages, LaTex, 7 eps figures, 2 table

M-theory on AdS_4xM^{111}: the complete Osp(2|4)xSU(3)xSU(2) spectrum from harmonic analysis

We reconsider the Kaluza Klein compactifications of D=11 supergravity on AdS_4x(G/H)_7 manifolds that were classified in the eighties, in the modern perspective of AdS_4/CFT_3 correspondence. We focus on one of the three N=2 cases: (G/H)_7=M^{111}=SU(3)xSU(2)xU(1)/SU(2)xU(1)'xU(1)''. Relying on the systematic use of the harmonic analysis techniques developed in the eighties by one of us (P. Fre') with R. D'Auria, we derive the complete spectrum of long, short and massless Osp(2|4)xSU(3)xSU(2) unitary irreducible representations obtained in this compactification. Our result also provides a general scheme for the other N=2 compactifications. Furthermore, it is a necessary comparison term in the AdS_4/CFT_3 correspondence: the complete AdS/CFT match of the spectra that we obtain will provide a much more stringent proof of the AdS/CFT correspondence than in the S^7 case, since the structure of the superconformal field theory on the M2-brane world volume must be such as to reproduce, at the level of composite operators, the flavor group representations, the conformal dimensions and the hypercharges that we obtain in the present article. The investigation of the match is left to future publications. Here we provide an exhaustive construction of the Kaluza Klein side of our spectroscopy.Comment: 65 page