On the problem of spacetime symmetries in the theory of supergravity

In the framework of the simple (N=1) supergravity, a definition of a spacetime symmetry is discussed. It is shown to have a smooth relativistic limit. As an application, the problem of the plane wave in supergravity is studied.Research Fellow at the Belgian National Fund for Scientific Research (FNRS).     

On the problem of spacetime symmetries in the theory of supergravity. III. Superspace formalism

The study of the problem of defining, in the theory of supergravity, the notion of a spacetime symmetry is continued. The connection with the formalism of superspace is explicitly considered, and the geometrical significance of the definition given in Parts I and II of this series of papers is emphasized.     

The problem of space-time symmetries in the theory of supergravity. Part V: Weak-field Birkhoff theorem in simple supergravity

It is established, within a weak-field approximation, that a spherically symmetric solution of Simple Supergravity (with the appropriate conditions on the orbits of the symmetry generators) admits necessarily the additional symmetry of translation in time, thus generalising the Birkhoff theorem of General Relativity.     

Supercovariant derivatives,super-Weyl groups,and N = 2 supergravity

We analyze the kinematic constraints for N = 2 Poincaré supergravity within the context of “superconformal symmetry breakdown”. We find that N = 2 supergravity is described in terms of two independent supertensors: W_αβij and T_αi. We also discuss general properties of superspace covariant derivatives to derive the relation of superspace to component approaches.     

Extended supergravity on the supergroup manifold: N = 3 and N = 2 theories

In this paper I construct the group-manifold first-order formulation of N = 2 and N = 3 supergravity based on the $\text{Osp}\text{(}\text{4}\text{2}\text{)}\text{and Osp}\text{(}\text{4}\text{3}\text{)}$ supergroups, respectively. In the case N = 2, a group manifold version of the theory was already presented in a previous paper. Here a simpler formulation is given which shows exact factorization in the SO(2) subgroup absent in the previous one. Particular attention is paid to the algebraic role played by the $\text{spin}\text{-}\text{1}\text{2}$ field which is the novel feature of the N = 3 case with respect to N = 2. It is shown how the “non-geometrical” term in the gravitino transformation law in the N = 2 theory arises from the rheonomic symmetry mechanism.     

SL(2,C)-gauge theory,N=1 supergravity and torsion

It is shown that the SL(2,C)-gauge theory of gravitation may be considered to correspond toN = 1 supergravity and the conserved current gives rise to the Einstein-Cartan action. The torsion term here appears due to the spinorial variable, which is associated with the internal helicity giving rise to the isospin algebra from the conformal reflection group. In this sense, the internal symmetry of hadrons is found to take a dominant role in gravitational phenomena in the microlocal space-time region where the Einstein-Cartan action becomes significant.     

Use of compensators to break supersymmetry in an N = 1 supergravity theory

We consider an N = 1 supergravity theory with multiple compensators and show that supersymmetry is broken by a solution to the equation of motion of a compensator. When a chiral scalar superfield is coupled to supergravity, we discuss various aspects of supersymmetry breaking and show that the super-Higgs-Kibble effect is operative. Possible applications of this mechanism of supersymmetry breaking in model building and extended supergravity theories are indicated.     

Wavefunction of the universe for N=2 6D supergravity

The wavefunction of the universe for N=2 6D supergravity is calculated numerically using a minisuperspace approach. When compared with the solution of the classical equations it is found that the resulting evolution of the universe is of Friedmann form with the radius of the internal space performing damped oscillations about a constant value.     

Space-time symmetries in the theory of supergravity,IV: Comparison between space-time and superspace formalisms

The two possible definitions, proposed in Parts II and III, of a space-time symmetry in supergravity, arising respectively from an analysis in four-dimensional space-time and from superspace considerations, are shown to be inequivalent, although closely related to one another. It is argued that the former must be preferred to the latter for physical reasons.     

Linearized N = 2 supergravity in terms of SU(2)-extended superfields

The linearized theory of N = 2 conformai supergravity is expressed in terms of a single irreducible SU(2)-extended superfield. In particular, in this way the origin of the N = 2 superconformal multiplet is established.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, No. 5, pp. 93–95, May, 1986.     

N = 3 and N = 1 supersymmetry in a new class of solutions for d = 11 supergravity

We present a new class of compactifying solutions for d = 11 supergravity. The internal 7-spaces are described by coset manifolds N^pqr of the form SU(3) × U(1)/U(1) × U(1). The three integers p, q, r characterize the embedding of the stability subgroup U(1) × U(1) in SU(3) × U(1).Their supersymmetry content is quite remarkable. For a particular choice of p, q, r the isometry of N^pqr is SU(3) × SU(2): in this case we find that N = 3 supersymmetry survives. For all the other values of p, q, r, supersymmetry is broken to N = 1, and the isometry group is SU(3) × U(1).We also find a class of solutions with internal photon curl F_αβγδ ≠ 0, breaking all supersymmetries.     

Linearized N=2 Poincaré supergravity in terms of SU(2)-extended superfields

Linearized Poincaré N=2 supergravity is presented in terms of SU(2)-extended superfields. Thus, the connection of SU(2)-extended superfields with the structure of auxiliary fields in N=2 supergravity is established.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 31–34, October, 1986.     

N = 8 supergravity in various dimensions and the implications for four dimensions

The possibilities for constructing new spontaneously broken N = 8 supergravity theories in four dimensions by applying the generalized dimensional reduction method to symmetrical theories in higher dimensions are explored.     

The Jordan Pair content of the magic square and the geometry of the scalars in N=2 supergravity

The close connection between Jordan and Lie algebras makes these Jordan structures of interest to physicists. The Freudenthal-Tits Magic Square, which exemplifies this connection, has recently entered into constructing supergravity. We show how Jordan pairs-which are, from several points of view, a most natural Jordan structure-are imbedded in the Magic Square. We compare our approach with that of Gürsey and show show the Hermitian symmetric spaces parametrized by the scalars of N=2, d=4 supergravity theories are related either to Jordan pairs or to geometries of projective dimension two, whose elements belong to a Jordan pair.     

On a Lie group of infinite order as a nontrivial coupling of an intrinsic and space-time symmetries II

A real Lie algebra of denumerable infinite order that contains as subalgebras the Poincaré algebraP and the algebraSU(3) is derived by the method introduced in [1]. A nontrivial mass formula is obtained.