B. de Wit

Special geometry, cubic polynomials and homogeneous quaternionic spaces

The existing classification of homogeneous quaternionic spaces is not complete. We study these spaces in the context of certainN=2 supergravity theories, where dimensional reduction induces a mapping betweenspecial real, Kähler and quaternionic spaces. The geometry of the real spaces is encoded in cubic polynomials, those of the Kähler and quaternionic manifolds in homogeneous holomorphic functions of second degree. We classify all cubic polynomials that have an invariance group that acts transitively on the real manifold. The corresponding Kähler and quaternionic manifolds are then homogeneous. We find that they lead to a well-defined subset of the normal quaternionic spaces classified by Alekseevskiî (and the corresponding special Kähler spaces given by Cecotti), but there is a new class of rank-3 spaces of quaternionic dimension larger than 3. We also point out that some of the rank-4 Alekseevskiî spaces were not fully specified and correspond to a finite variety of inequivalent spaces. A simpler version of the equation that underlies the classification of this paper also emerges in the context ofW3 algebras.

Structure of N=2 Supergravity

A number of N = 2 superconformal multiplets are presented. A corresponding calculus exists which can be exploited for the construction of superconformally invariant actions. Actions that are invariant under Poincare and de Sitter supersymmetry are then obtained by imposing a suitable set of gauge conditions. It is shown that there exist two inequivalent off-shell formulations of N = 2 Poincare and de Sitter supergravity.

Locally supersymmetric D = 3 non-linear sigma models

Abstract We study non-linear sigma models with N local supersymmetries in three space-time dimensions. For N = 1 and 2 the target space of these models is riemannian or Kahler, respectively. All N > 2 theories are associated with Einstein spaces. For N = 3 the target space is quaternionic, while for N = 4 it generally decomposes into two separate quaternionic spaces, associated with inequivalent supermultiplets. For N = 5, 6, 8 there is a unique (symmetric) space for any given number of supermultiplets. Beyond that there are only theories based on a single supermultiplet for N = 9, 10, 12 and 16, associated with coset spaces with the exceptional isometry groups F 4(−20) , E 6(−14) , E 7(−5) and E 8(+8) , respectively. For N = 3 and N ⩾ 5 the D = 2 theories obtained by dimensional reduction are two-loop finite.

Covariant Quantization of Gauge Theories with Open Gauge Algebra

Abstract We show that when the algebra of gauge transformations is not closed one can still generally define an effective action that is invariant under an appropriate extension of the Becchi-Rouet-Stora transformations. Both the action and transformation rules contain terms of higher order in the ghost fields. The generalized Ward identifies imply the existence of a gauge-independent S matrix. Nilpotency of extended BRS transformations is regained upon use of the full field equations of ghost and ordinary fields.

The auxiliary field structure in chirally extended supergravity

Abstract The auxiliary fields for Einstein supergravity with axial gauge coupling are those of Maxwell-Einstein supergravity. The gauge algebra is an irreducible extension of the gauge algebra of Einstein supergravity, so that the complete system is a gauge theory with an extra local chiral invariance, rather than a matter coupling.

Two loop finiteness of D = 2 supergravity

We establish two-loop (on-shell) finiteness of certain supergravity theories in two dimensions. Possible implications of this result are discussed.

Covariant quantization of supergravity

Abstract Recently noted modifications of the quantization rules for supergravity can be understood within the framework of conventional covariant quantization, proveded one uses a formulation of the theory in which the supersymmetry algebra closes. Using such a formulation due to Breitenlohner we discuss the quantization, and are naturally led to terms quartic in the ghost fields in the quantum action.

Auxiliary fields and ultraviolet divergences in supergravity

Abstract The relation between the supergravity counterterms and the coupling of auxiliary fields to matter is investigated. As a result we determine the infinities due to one and two internal-matter loops for the supersymmetric Yang-Mills-Einstein system. Furthermore, the couplings of the auxiliary fields to the massive scalar multiplet are obtained through order ϰ 2 , and the contribution to the counterterm Lagrangian trilinear in the auxiliary fields is given.