Davide Fabbri

3D superconformal theories from Sasakian seven-manifolds: New non-trivial evidences for AdS4/CFT3

Abstract 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.

The Osp(8∥4) singleton action from the supermembrane☆☆☆

Abstract Our goal is to study the supermembrane on an AdS 4 × M 7 background, where M 7 is a seven-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 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 realized superconformal transformations. To do this we introduce the supergroup generalization of the solvable Lie algebra parametrization 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 realized as a free field theory living on flat Minkowski space.

Shadow multiplets in AdS4/CFT3 and the super-Higgs mechanism☆

Abstract We discuss a general pairing that occurs in compactifications of M-theory on AdS 4 ×X 7 backgrounds between massless ultra short multiplets and their massive shadows, namely certain universal long multiplets with fixed protected dimensions. In particular, we consider the shadow of the short graviton multiplet in N =3 compactifications. It turns out to be a massive spin- 3/2 multiplet with scale dimension E 0 =3 and with the quantum numbers of a super-Higgs multiplet. Hence each N =3 AdS 4 ×X 7 vacuum is actually to be interpreted as a spontaneously broken phase of an N =4 theory. Comparison with standard gauged N =4 supergravity in 4 dimensions reveals the unexpected bound E 0 on the dimension of the broken gravitino multiplet. This hints to the existence of new versions of extended supergravities, in particular N =4 where such upper bounds are evaded and where all possible vacua have a reduced supersymmetry N 0 N . We name them shadow supergravities. In particular, using arguments based on the solvable Lie algebra parametrization of the scalar manifold, we discuss the possible structure of shadow N =4 supergravity. Using our previous results on the SCFT dual of the AdS 4 ×N 0,1,0 vacuum we discuss the SCFT realization of the universal N =3 shadow multiplet. RG flows from an N =4 to an N =3 phase are ruled out by the fact that the N =4 vacuum is at infinite distance in moduli space, denoting the presence of a topology change.We discuss a general pairing that occurs in compactifications of M-theory on AdS_4 x X^7 backgrounds between massless ultra short multiplets and their massive shadows, namely certain universal long multiplets with fixed protected dimensions. In particular we consider the shadow of the short graviton multiplet in N=3 compactifications. It turns out to be a massive spin 3/2 multiplet with scale dimension E_0=3 and with the quantum numbers of a super-Higgs multiplet. Hence each N=3 AdS_4 x X^7 vacuum is actually to be interpreted as a spontaneously broken phase of an N=4 theory. Comparison with standard gauged N=4 supergravity in 4 dimensions reveals the unexpected bound E_0<3 on the dimension of the broken gravitino multiplet. This hints to the existence of new versions of extended supergravities, in particular N=4 where such upper bounds are evaded and where all possible vacua have a reduced supersymmetry N_0<N. We name them shadow supergravities. In particular, using arguments based on the solvable Lie algebra parametrization of the scalar manifold, we discuss the possible structure of shadow N=4 supergravity. Using our previous results on the SCFT dual of the AdS_4 x N^{0,1,0} vacuum we discuss the SCFT realization of the universal N=3 shadow multiplet. RG flows from an N=4 to an N=3 phase are ruled out by the fact that the N=4 vacuum is at infinite distance in moduli space, denoting the presence of a topology change.

Three dimensional Conformal Field Theories from Sasakian seven-manifolds

We present the construction of the candidate conformal field theories dual to

Osp(|4) supermultiplets as conformal superfields on AdS4 and the generic form of = 2, d = 3 gauge theories

AdS_4

Osp(script N|4) supermultiplets as conformal superfields on ∂ AdS4 and the generic form of script N = 2, d = 3 gauge theories

non-maximally supersymmetric compactifications of 11D supergravity. We compare the spectra of the two theories and discuss the realization of the baryonic symmetries. Finally we comment on the presence in the spectrum of long multiplets with rational energies, trying to explain their existence.

The Osp(8|4) singleton action from the super membrane

In this paper we fill a necessary gap in order to realize an explicit comparison between the Kaluza-Klein spectra of supergravity compactified on AdS 4 × X 7 and superconformal field theories living on the worldvolume of M2-branes. On the algebraic side we consider the superalgebra Osp ( | 4) and we study the double interpretation of its unitary irreducible representations either as supermultiplets of particle states in the bulk or as a conformal superfield on the boundary. On the Lagrangian field theory side we construct, using rheonomy rather than superfield techniques, the generic form of an = 2, d = 3 gauge theory. Indeed, the superconformal multiplets are supposed to be composite operators in a suitable gauge theory.

The Singleton action from the supermembrane

In this paper we fill a necessary gap in order to realize an explicit comparison between the Kaluza-Klein spectra of supergravity compactified on AdS 4 × X 7 and superconformal field theories living on the worldvolume of M2-branes. On the algebraic side we consider the superalgebra Osp ( | 4) and we study the double interpretation of its unitary irreducible representations either as supermultiplets of particle states in the bulk or as a conformal superfield on the boundary. On the Lagrangian field theory side we construct, using rheonomy rather than superfield techniques, the generic form of an = 2, d = 3 gauge theory. Indeed, the superconformal multiplets are supposed to be composite operators in a suitable gauge theory.

M-theory on AdS4 × M111: the complete Osp(2|4) × SU(3) × SU(2) spectrum from harmonic analysis☆

We derive the free Osp(8|4) singleton action by sending the M2brane to the Minkowski boundary of an AdS_4x{\cal M}_7 background. We do this by means of the solvable Lie algebra parametrization of the coset space. We also give some comments on singleton actions from membranes on AdS_4xG/H backgrounds.

THE OSP(84) SINGLETON ACTION FROM THE SUPERMEMBRANE

We derive the free Osp(8|4) singleton action by sending the M2brane to the Minkowski boundary of an AdS_4x{\cal M}_7 background. We do this by means of the solvable Lie algebra parametrization of the coset space. We also give some comments on singleton actions from membranes on AdS_4xG/H backgrounds.