arXiv subjects
Publications and source records attributed to Pietro Fre'.
We derive from a general formulation of pure spinor string theory on type IIA backgrounds the specific form of the action for the AdS_4 x P^3 background. We provide a complete geometrical characterization of the structure of the superfields involved in the action.
We show the equivalence of the different types of pure spinor constraints geometrically derived from the Free Differential Algebras of N=2 d=10 supergravities. Firstly, we compute the general solutions of these constraints, using both a G_2 and an SO(8) covariant decomposition of the 10d chiral spinors. Secondly, we verify that the number of independent degrees of freedom is equal to that implied by the Poincare' pure spinor constraints so-far used for superstrings, namely twenty two. Thirdly, we show the equivalence between the FDA type IIA/B constraints among each other and with the Poincare' ones.
We organize the homogeneous special geometries, describing as well the couplings of D=6, 5, 4 and 3 supergravities with 8 supercharges, in a small number of universality classes. This relates manifolds on which similar types of dynamical solutions can exist. The mathematical ingredient is the Tits-Satake projection of real simple Lie algebras, which we extend to all solvable Lie algebras occurring in these homogeneous special geometries. Apart from some exotic cases all the other, 'very special', homogeneous manifolds can be grouped in seven universality classes. The organization of these classes, which capture the essential features of their basic dynamics, commutes with the r- and c-map. Different members are distinguished by different choices of the paint group, a notion discovered in the context of cosmic billiard dynamics of non maximally supersymmetric supergravities. We comment on the usefulness of this organization in universality classes both in relation with cosmic billiard dynamics and with configurations of branes and orbifolds defining special geometry backgrounds.
The lagrangian formalism for the supermembrane in any 11d supergravity background is constructed in the pure spinor framework. Our gauge-fixed action is manifestly BRST, supersymmetric, and 3d Lorentz invariant. The relation between the Free Differential Algebras (FDA) underlying 11d supergravity and the BRST symmetry of the membrane action is exploited. The "gauge-fixing" has a natural interpretation as the variation of the Chevalley cohomology class needed for the extension of 11d super-Poincare' superalgebra to M-theory FDA. We study the solution of the pure spinor constraints in full detail.
The derivation of smooth cosmic billiard solutions through the compensator method is extended to non maximal supergravities. A new key feature is the non-maximal split nature of the scalar coset manifold. To deal with this, one needs the theory of Tits Satake projections leading to maximal split projected algebras. Interesting exact solutions that display several smooth bounces can thus be derived. From the analysis of the Tits Satake projection emerges a regular scheme for all non maximal supergravities and a challenging so far unobserved structure, that of the paint group G-paint. This latter is preserved through dimensional reduction and provides a powerful tool to codify solutions. It appears that the dynamical walls on which the cosmic ball bounces come actually in painted copies rotated into each other by G-paint. The effective cosmic dynamics is that dictated by the maximal split Tits Satake manifold plus paint. We work out in details the example provided by N=6,D=4 supergravity, whose scalar manifold is the special Kahlerian SO*(12)}/SU(6)xU(1). In D=3 it maps to the quaternionic E_7(-5)/ SO(12) x SO(3). From this example we extract a scheme that holds for all supergravities with homogeneous scalar manifolds and that we plan to generalize to generic special geometries. We also comment on the merging of the Tits-Satake projection with the affine Kac--Moody extensions originating in dimensional reduction to D=2 and D=1.
In this paper we study the systematics of the affine extension of supergravity duality algebras when we step down from D=4 to D=2. For all D=4 supergravities (with N >= 3) there is a universal field theoretical mechanism promoting the extension, which relies on the coexistence of two non locally related lagrangian descriptions. This provides a Chevalley-Serre presentation of the affine Kac Moody algebra which follows a universal pattern for all supergravities and is an extension of the mechanism considered by Nicolai for pure N=1 supergravity. There are new distinctive features in extended theories related to the presence of vector fields and to their symplectic description. The novelty is that in supergravity the so named Matzner-Missner description is structurally different from the Ehlers one with gauge 0--forms subject to SO(2n,2n) electric--magnetic duality rotations representing in D=2 the Sp(2n,R) rotations of D=4. The role played by the symplectic bundle of vectors is emphasized in view of implementing the affine extension also in N=2 supergravity, where the scalar manifold is not necessarily a homogeneous manifold U/H. We show that the mechanism of the affine extension commutes with the Tits Satake projection of the duality algebras. This is very important for the issue of cosmic billiards. We also comment on the general field theoretical mechanism of the further hyperbolic extension obtained in D=1. The possible uses of our results and their relation to outstanding problems are pointed out.
The FDA algebras emerging from twisted tori compactifications of M-theory with fluxes are discussed within the general classification scheme provided by Sullivan's theorems and by Chevalley cohomology. It is shown that the generalized Maurer Cartan equations which have appeared in the literature, in spite of their complicated appearance, once suitably decoded within cohomology, lead to trivial FDA.s, all new p--form generators being contractible when the 4--form flux is cohomologically trivial. Non trivial D=4 FDA.s can emerge from non trivial fluxes but only if the cohomology class of the flux satisfies an additional algebraic condition which appears not to be satisfied in general and has to be studied for each algebra separately. As an illustration an exhaustive study of Chevalley cohomology for the simplest class of SS algebras is presented but a general formalism is developed, based on the structure of a double elliptic complex, which, besides providing the presented results, makes possible the quick analysis of compactification on any other twisted torus.
In the previous submission of this paper we claimed to have solved the problem of constructing a consistent non-abelian Born Infeld action which is $κ$--supersymmetric to all orders. Our method was based on an extension of target superspace to $\mathrm{N} \times \mathrm{N}$ matrix--valued objects for all the items appearing in the geometric construction. Then we applied the \textit{double first order formalism} introduced by us in the previous construction of abelian brane actions to the non--abelian case and we claimed that the Bosonic action given by the prescription of the \textit{symmetrized trace} could be promoted to a fully kappa supersymmetric one. Unfortunately there is an internal inconsistency, relative to U(N) gauge invariance in the matricisation of target superspace geometry and there is a subtle inconsistency in the variation of the symmetric trace action due to the loss of associativity of the underlying symmetrized product. Because of that the entire construction previously submitted does not stand on its feet. Consequently the present resubmission is done in order to disclaim our previously claimed result and also to express our sincere gratitude to our friends Paul Howe and Ulf Lindstrom who, with their constructive criticism and private correspondence, have helped us to understand where the bugs in our construction were.
In the present talk I shall review the construction of N=2 supergravity models exhibiting stable de Sitter vacua. These solutions represent the first instance of stable backgrounds with positive cosmological constant in the framework of extended supergravities (N >=2). After briefly reviewing the role of de Sitter space--times in inflationary cosmology, I shall describe the main ingredients which were necessary for the construction of gauged N=2 supergravity models admitting stable solutions of this kind.
The recent construction of the non-semisimple gaugings of maximal D=5 supergravity is reported here. This construction is worked out in the so-called rheonomic approach, based on Free Differential Algebras and the solution of their Bianchi identities. In this approach the dualization mechanism between one-forms and two-forms is more transparent. The lagrangian is unnecessary since the field equations follow from closure of the supersymmetry algebra. These theories contain 12-r self-dual two-forms and 15+r gauge vectors, r of which are abelian and neutral. Such theories, whose existence has been proved and their supersymmetry algebra constructed, have potentially interesting properties in relation with domain wall solutions and the trapping of gravity.
In this paper we discuss candidate superconformal N=2 gauge theories that realize the AdS/CFT correspondence with M--theory compactified on the homogeneous Sasakian 7-manifolds M^7 that were classified long ago. In particular we focus on the two cases M^7=Q^{1,1,1} and M^7=M^{1,1,1}, for the latter the Kaluza Klein spectrum being completely known. We show how the toric description of M^7 suggests the gauge group and the supersingleton fields. The conformal dimensions of the latter can be independently calculated by comparison with the mass of baryonic operators that correspond to 5-branes wrapped on supersymmetric 5-cycles and are charged with respect to the Betti multiplets. The entire Kaluza Klein spectrum of short multiplets agrees with these dimensions. Furthermore, the metric cone over the Sasakian manifold is a conifold algebraically embedded in some C^p. The ring of chiral primary fields is defined as the coordinate ring of C^p modded by the ideal generated by the embedding equations; this ideal has a nice characterization by means of representation theory. The entire Kaluza Klein spectrum is explained in terms of these vanishing relations. We give the superfield interpretation of all short multiplets and we point out the existence of many long multiplets with rational protected dimensions, whose presence and pattern seem to be universal in all compactifications.
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.
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.
Our goal is to study the supermembrane on an $AdS_4 \times \cal M_7$ background, where $\cal M_7$ is a 7--dimensional Einstein manifold with $N$ Killing spinors. This is a direct way to derive the $Osp(N|4)$ singleton field theory with all the additional properties inherited from the geometry of the internal manifold. As a first example we consider the maximally supersymmetric $Osp(8|4)$ singleton corresponding to the choice $\cal M_7 = S^7$. We find the explicit form of the action of the membrane coupled to this background geometry and show its invariance under non--linearly realised superconformal transformations. To do this we introduce a supergroup generalisation of the solvable Lie algebra parametrisation of non--compact coset spaces. We also derive the action of quantum fluctuations around the classical configuration, showing that this is precisely the singleton action. We find that the singleton is simply realised as a free field theory living on flat Minkowski space.
In this talk I review both accomplished results and work in progress on the use of solvable Lie algebras as an intrinsic algebraic characterization of the scalar field sector of M--theory low energy effective lagrangians. In particular I review the application of these techniques in obtaining the most general form of BPS black hole solutions.
In this lecture I review recent results on the first order equations describing BPS extremal states, in particular N=2 extremal black-holes. The role of special geometry is emphasized also in the rigid theory and a comparison is drawn with the supersymmetric derivation of instantons and hyperinstantons in topological field theories. Work in progress on the application of solvable Lie algebras to the discussion of BPS states in maximally extended supergravities is outlined.
The monopole equations in the dual abelian theory of the N=2 gauge-theory, recently proposed by Witten as a new tool to study topological invariants, are shown to be the simplest elements in a class of instanton equations that follow from the improved topological twist mechanism introduced by the authors in previous papers. When applied to the N=2 sigma-model, this twisting procedure suggested the introduction of the so-called hyperinstantons, or triholomorphic maps. When gauging the sigma-model by coupling it to the vector multiplet of a gauge group G, one gets gauged hyperinstantons that reduce to the Seiberg-Witten equations in the flat case and G=U(1). The deformation of the self-duality condition on the gauge-field strength due to the monopole-hyperinstanton is very similar to the deformation of the self-duality condition on the Riemann curvature previously observed by the authors when the hyperinstantons are coupled to topological gravity. In this paper the general form of the hyperinstantonic equations coupled to both gravity and gauge multiplets is presented.
We derive a model of constrained topological gravity, a theory recently introduced by us through the twist of N=2 Liouville theory, starting from the general BRST algebra and imposing the moduli space constraint as a gauge fixing. To do this, it is necessary to introduce a formalism that allows a careful treatment of the global and the local degrees of freedom of the fields. Surprisingly, the moduli space constraint arises from the simplest and most natural gauge-fermion ({\sl antighost} $\times$ {\sl Lagrange multiplier}), confirming the previous results. The simplified technical set-up provides a deeper understanding for constrained topological gravity and a convenient framework for future investigations, like the matter coupling and the analysis of the effects of the constraint on the holomorphic anomaly.