Piet Termonia

N = 8 gaugings revisited: an exhaustive classification

In this paper we reconsider, for N = 8 supergravity, the problem of gauging the most general electric subgroup. We show that admissible theories are fully characterized by a single algebraic equation to be satisfied by the embedding Ggauge → SL(8, R) ⊂ E7(7). The complete set of solutions to this equation contains 36 parameters. Modding by the action of SL(8, R) conjugations that yield equivalent theories all continuous parameters are eliminated except for an overall coupling constant and we obtain a discrete set of orbits. This set is in one-to-one correspondence with 36 Lie subalgebras of SL(8, R), corresponding to all possible real forms of the SO(8) Lie algebra plus a set of contractions thereof. By means of our analysis we establish the theorem that the N = 8 gaugings constructed by Hull in the middle eighties constitute the exhaustive set of models. As a corollary we show that there exists a unique seven-dimensional abelian gauging. The corresponding abelian algebra is not contained in the maximal abelian ideal of the solvable Lie algebra generating the scalar manifold E7(7)/SU(8)

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.

N = 2 supergravity Lagrangians with vector-tensor multiplets

We discuss the coupling of vector-tensor multiplets to N = 2 supergravity.

The vector-tensor supermultiplet with gauged central charge

The vector-tensor multiplet is coupled off-shell to an N = 2 vector multiplet such that its central charge transformations are realized locally. A gauged central charge is a necessary prerequisite for a coupling to supergravity and the strategy underlying our construction uses the potential for such a coupling as a guiding principle. The results for the action and transformation rules take a nonlinear form and necessarily include a Chern-Simons term. After a duality transformation the action is encoded in a homogeneous holomorphic function consistent with special geometry.

The structure of N=3 multiplets in AdS4 and the complete Osp(3|4)×SU(3) spectrum of M-theory on AdS4×N0,1,0

Abstract In this paper, relying on previous results of one of us on harmonic analysis, we derive the complete spectrum of Osp(3|4)×SU(3) multiplets that one obtains compactifying D=11 supergravity on the unique homogeneous space N0,1,0 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 smax≤2.

Chern-Simons Couplings and Inequivalent Vector-Tensor Multiplets

The off-shell vector-tensor multiplet is considered in an arbitrary background of N = 2 vector supermultiplets. We establish the existence of two inequivalent versions, characterized by different Chern-Simons couplings. In one version the vector field of the vector-tensor multiplet is contained quadratically in the Chem-Simons term, which implies non-linear terms in the supersymmetry transformations and equations of motion. In the second version, which requires a background of at least two abelian vector supermultiplets, the supersymmetry transformations remain at most linear in the vector-tensor components. This version is of the type known to arise from reduction of tensor supermultiplets in six dimensions. Our work applies to any number of vector-tensor multiplets.

The complete N=3 Kaluza–Klein spectrum of 11D supergravity on AdS4×N010☆

We derive the invariant operators of the zero-form, the one-form, the two-form and the spinor from which the mass spectrum of Kaluza Klein of eleven-dimensional supergravity on AdS4 × N 010 can be derived by means of harmonic analysis. We calculate their eigenvalues for all representations of SU(3) × SO(3). We show that the information contained in these operators is sufficient toreconstruct the complete N = 3 supersymmetry content of the compactified theory. We find the N = 3 massless graviton multiplet, the Betti multiplet and the SU(3) Killing vector multiplet.

The Complete N=3 Kaluza-Klein spectrum of 11-D supergravity on AdS(4) x N** 010

We derive the invariant operators of the zero-form, the one-form, the two-form and the spinor from which the mass spectrum of Kaluza Klein of eleven-dimensional supergravity on AdS4 × N 010 can be derived by means of harmonic analysis. We calculate their eigenvalues for all representations of SU(3) × SO(3). We show that the information contained in these operators is sufficient toreconstruct the complete N = 3 supersymmetry content of the compactified theory. We find the N = 3 massless graviton multiplet, the Betti multiplet and the SU(3) Killing vector multiplet.

The complete Kaluza–Klein spectrum of supergravity on

We derive the invariant operators of the zero-form, the one-form, the two-form and the spinor from which the mass spectrum of Kaluza Klein of eleven-dimensional supergravity on AdS4 × N 010 can be derived by means of harmonic analysis. We calculate their eigenvalues for all representations of SU(3) × SO(3). We show that the information contained in these operators is sufficient toreconstruct the complete N = 3 supersymmetry content of the compactified theory. We find the N = 3 massless graviton multiplet, the Betti multiplet and the SU(3) Killing vector multiplet.

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

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.