Pietro Fré

Geometric supergravity in D=11 and its hidden supergroup

Abstract In this paper we address two questions: the geometrical formulation of D = 11 supergravity and the derivation of the super Lie algebra it is based on. The solutions of the two problems are intimately related and are obtained via the introduction of the new concept of a Cartan integrable system described in this paper. The previously developed group manifold framework can be naturally extended to a Cartan integrable system manifold approach. Within this scheme we obtain a geometric action for D = 11 supergravity based on a suitable Cartan system. This latter turns out to be a compact description of a two-element class of supergroups containing, besides Lorentz J ab , translation P a and ordinary supersymmetry Q , the following extra generators: two- and five-index skew-symmetric tensors Z a 1 a 2 , Z a 1… a 5 and a further spinorial charge Q ′ . Q ′ commutes with itself and everything J ab . It appears in the commutators of Q with P a , Z a 1 a 2 , Z a 1 … a 5.

Special and quaternionic isometries: General couplings in N = 2 supergravity and the scalar potential☆

Abstract The general lagrangian for N = 2 matter-coupled supergravity is obtained, by gauging general isometries of quaternionic manifolds which can be coupled to supergravity. The resulting theories are purely geometrical and give an interplay between quaternionic and special Kahler geometry. The resulting scalar potential is expressed in terms of the two Killing prepotentials of the two geometries and it may be relevant to study transitions between different vacua in superstring theory. Furthermore from the geometrical point of view the prepotentials are hamiltonian functions yielding a poissonian realization of the gauge algebra on both the special Kahler and the quaternionic manifold. A possible cohomological obstruction to this realization is pointed out.

Pure Spinor Formalism for Osp(N |4) backgrounds

We start from the Maurer-Cartan (MC) equations of the Osp(N |4) superalgebras satisfied by the left-invariant super-forms realized on supercoset manifolds of the corresponding supergroups and we derive some new pure spinor constraints. They are obtained by ”ghostifying” the MC forms and extending the differential d to a BRST differential. From the superalgebras b G = Osp(N |4) we single out different

G / H M-branes and AdS(p+2) geometries

We discuss the class of BPS saturated M-branes that are in one-to-one correspondence with the Freund-Rubin compactifications of M-theory on either AdS4 × G/H or AdS7 × G/H, where G/H is any of the seven (or four) dimensional Einstein coset manifolds with Killing spinors classified long ago in the context of Kaluza-Klein supergravity. These G/H M-branes, whose existence was previously pointed out in the literature, are solitons that interpolate between flat space at infinity and the old Kaluza-Klein compactifications at the horizon. They preserve N/2 supersymmetries where N is the number of Killing spinors of the AdS × G/H vacuum. A crucial ingredient in our discussion is the identification of a solvable Lie algebra parametrization of the Lorentzian noncompact coset SO(2, p + 1)/SO(1, p + 1) corresponding to anti-de Sitter space AdSp + 2. The solvable coordinates are those naturally emerging from the near horizon limit of the G/H p-brane and correspond to the Bertotti-Robinson form of the anti-de Sitter metric. The pull-back of anti-de Sitter isometries on the p-brane world-volume contain, in particular, the recently found broken conformal transformations

Rings of short N=3 superfields in three-dimensions and M theory on AdS(4) x N**(0,1,0)

In this paper we investigate three-dimensional superconformal gauge theories with = 3 supersymmetry. Independently from specific models, we derive the shortening conditions for unitary representations of the Osp(3|4) superalgebra and we express them in terms of differential constraints on three-dimensional = 3 superfields. We find a ring structure underlying these short representations, which is just the direct generalization of the chiral ring structure of = 2 theories. When the superconformal field theory is realized on the worldvolume of an M2-brane such a superfield ring is the counterpart of the ring defined by the algebraic geometry of the eight-dimensional cone transverse to the brane. This and other arguments identify the = 3 superconformal field theory dual to M-theory compactified on AdS4×N0,1,0. It is an = 3 gauge theory with SU(N)×SU(N) gauge group coupled to a suitable set of hypermultiplets, with an additional Chern-Simons interaction. The AdS/CFT correspondence can be verified directly using the recently worked out Kaluza-Klein (KK) spectrum of N0,1,0 and we find a perfect match. We also note that besides the usual set of BPS conformal operators dual to the lightest KK states, we find that the composite operators corresponding to certain massive KK modes are organized into a massive spin-3/2 = 3 multiplet that might be identified with the super-Higgs multiplet of a spontaneously broken = 4 theory. We investigate this intriguing and inspiring feature in a separate paper.

Twisted N=2 supergravity as topological gravity in four dimensions

Abstract We show that the BRST quantum version of pure D = 4 N = 2 supergravity can be topologically twisted, to yield a formulation of topological gravity in four dimensions. The topological BRST complex is just a re-arrangement of the old BRST complex, that partly modifies the role of physical and ghost fields: indeed, the new ghost number turns out to be the sum of the old ghost number plus the internal U(1) charge. Furthermore, the action of N = 2 supergravity is retrieved from topological gravity by choosing a gauge fixing that reduces the space of physical states to the space of gravitational instanton configurations, namely to self-dual spin connections. The descent equations relating the topological observables are explicitly exhibited and discussed. Ours is a first step in a programme that aims at finding the topological sector of matter coupled N = 2 supergravity, viewed as the effective lagrangian of type II superstrings and, as such, already related two-dimensional topological field theories. As it stands the theory we discuss may prove useful in describing gravitational instanton moduli-spaces.

Non-semisimple gaugings of D = 5, N = 8 supergravity and FDAs

We reformulate maximal D = 5 supergravity in the consistent approach uniquely based on free differential algebras and the solution of their Bianchi identities (i.e. the rheonomic method). In this approach the Lagrangian is unnecessary since the field equations follow from closure of the supersymmetry algebra. This enables us to explicitly construct the non-compact gaugings corresponding to the non-semisimple algebras CSO(p,q,r), irrespectively of the existence of a Lagrangian. The use of free differential algebras is essential to clarify, within a cohomological set-up, the dualization mechanism between 1- and 2-forms. Our theories contain 12-r self-dual 2-forms and 15 + r gauge vectors, r of which are Abelian and neutral. These theories, whose existence is proved and their supersymmetry algebra constructed hereby, have potentially interesting properties in relation to domain wall solutions and the trapping of gravity.

The 0-brane Action in a General D = 4 Supergravity Background

We begin by presenting the superparticle action in the background of = 2, D = 4 supergravity coupled to n vector multiplets interacting via an arbitrary special Kahler geometry. Our construction is based on implementing -supersymmetry. In particular, our result can be interpreted as the source term for = 2 BPS black holes with a finite horizon area. When the vector multiplets can be associated with the complex structure moduli of a Calabi-Yau manifold, our 0-brane action can then be derived by wrapping 3-branes around 3-cycles of the 3-fold. Our result can be extended to the case of higher supersymmetry; we explicitly construct the supersymmetric action for a superparticle moving in an arbitrary = 8 supergravity background with ½, (1/4) or (1/8) residual supersymmetry

A search for non-perturbative dualities of local N = 2 Yang - Mills theories from Calabi - Yau 3-folds

The generalization of the rigid special geometry of the vector multiplet quantum moduli space to the case of supergravity is discussed through the notion of a dynamical Calabi - Yau 3-fold. Duality symmetries of this manifold are connected with the analogous dualities associated with the dynamical Riemann surface of the rigid theory. N = 2 rigid gauge theories are reviewed in a framework ready for comparison with the local case. As a byproduct we give in general the full duality group (quantum monodromy) for an arbitrary rigid SU(r+1) gauge theory, extending previous explicit constructions for the r = 1,2 cases. In the coupling to gravity, R-symmetry and monodromy groups of the dynamical Riemann surface, whose structure we discuss in detail, are embedded into the symplectic duality group associated with the moduli space of the dynamical Calabi - Yau 3-fold.

Topological σ-models in four dimensions and triholomorphic maps

Abstract It is well known that topological σ-models in two dimensions constitute a path-integral approach to the study of holomorphic maps from a Riemann surface Σ to an almost complex manifold K , the most interesting case being that were K is a Kahler manifold. We show that, in the same way, topological σ-models in four dimensions introduce a path-integral approach to the study of triholomorphic maps q: M → N between a four-dimensional riemannian manifold M and an almost quaternionic manifold N . The most interesting cases are those where M, N are hyper-Kahler or quaternionic Kahler. BRST-cohomology translates into intersection theory in the moduli-space of this new class of instantonic maps, that are named hyperinstantons by us. The definition of triholomorphicity that we propose is expressed by the equation q ∗ − J u ∘ q ∗ ∘ j u = 0 , where { j u , u = 1,2,3} is an almost quaternionic structure on M and { J u , u = 1,2,3} is an almost quaternionic structure on N . This is a generalization of the Cauchy-Fueter equations. For M, N hyper-Kahler, this generalization naturally arises by obtaining the topological σ-model as a twisted version of the N = 2 globally supersymmetric σ-model. We discuss various examples of hyperinstantons, in particular on the torus and the K3 surface. We also analyze the coupling of the topological σ-model to topological gravity. The classification of triholomorphic maps and the analysis of their moduli-space is a new and fully open mathematical problem that we believe deserves the attention of both mathematicians and physicists.