Superconformal symmetry and maximal supergravity in various dimensions

Abstract

In this paper we explore the relation between conformal superalgebras with 64 supercharges and maximal supergravity theories in three, four and six dimensions using twistorial oscillator techniques. The massless fields of N = 8 supergravity in four dimensions were shown to fit into a CPT-self-conjugate doubleton supermultiplet of the conformal superalgebra SU (2, 2|8) a long time ago. We show that the fields of maximal supergravity in three dimensions can similarly be fitted into the super singleton multiplet of the conformal superalgebra OSp(16|4, R), which is related to the doubleton supermultiplet of SU (2, 2|8) by dimensional reduction.Moreover, we construct the ultra-short supermultiplet of the six-dimensional conformal superalgebra OSp(8 * |8) and show that its component fields can be organized in an on-shell superfield. The ultra-short OSp(8 * |8) multiplet reduces to the doubleton supermultiplet of SU (2, 2|8) upon dimensional reduction. We discuss the possibility of a novel non-metric based (4, 0) six-dimensional supergravity theory with U Sp (8) R-symmetry that reduces to maximal supergravity in four dimensions and is different from six-dimensional metric based (2, 2) maximal supergravity, whose fields cannot be fitted into a unitary supermultiplet of a simple conformal superalgebra.Such an interacting (4, 0) theory would be the non-metric gravitational analog of the interacting (2, 0) theory.

The fuzzy 4-hyperboloid Hn4 and higher-spin in Yang–Mills matrix models

“…The oscillator algebra (3.16) can be realized explicitly as follows (cf. [24,27]): Consider bosonic creation and annihilation operators a i , b j which satisfy…”

“…and the time-like generator X 0 (or the "conformal Hamiltonian" E) is given by Minireps. The simplest class of unitary representation has lowest weight space given by the Fock vacuum a i |0 = 0 = b i |0 , which defines [27] |Ω := |1, 0, 0 =:…”

“…We will ignore the dependence on two sheets M ± for simplicity 27. A gauge-invariant constraint would be (X a + A a )(X a + A a ) = −R 2 .…”

Six-dimensional superconformal couplings of non-abelian tensor and hypermultiplets

“…Let us finally mention other approaches towards the field equations [11,26,27] and amplitudes [28] of the (2,0) theory whose relation to the presented construction will be interesting to understand. We also want to mention possible relations two supergravity theories [30,31] The paper is organized as follows: In section 2 we discuss the geometrical background for the superconformal hypermultiplets. In section 3 we describe the Lagrangians for the hyper-and the tensor/vector system, respectively, and the embedding of the hypermultiplet gauging into the latter.…”

Supersymmetry constraints on U-duality invariant deformations of $$ \mathcal{N} $$ ≥ 5 supergravity

“…More specifically it was shown long ago that the fields of N = 8 supergravity can be fitted into the CPT self-conjugate doubleton supermultiplet of the N = 8 superconformal algebra SU (2, 2|8) [21]. Motivated by the work of [7] on the study of counterterms of maximal supergravity using this doubleton supermultiplet it was reformulated in terms of constrained superfields in [22]. The result of the investigation of [20] was that it is not possible to deform the maximal supergravity to restore E 7 (7) duality, while maintaining both general covariance and N = 8 supersymmetry, as was proposed in [2], if the required extra vector fields are assumed to be dynamical.…”