Formulation of 11-dimensional supergravity in superspace

We formulate on-shell 11-dimensional supergravity in superspace and express its equations of motion in terms of purely geometrical quantities. All torsion and curvature components are solved in terms of a single superfield W_rstu, totally antisymmetric in its (flat vector) indices. The dimensional reduction of this formulation is expected to be related to the superspace formulation of N=8 extended supergravity and might explain the origin of the hidden (local) SU(8) and (global) E₇ symmetries present in this theory.     

On superspace supergravity in ten dimensions

Off-shell N=1, d=10 supergravity splits into a (128+128)-component multiplet and two scalar superfields. A concise formulation of the superspace contraints corresponding to the (128+128)-multiplet is given and the incorporation of the dimension - 6 scalar superfield discussed at the linearized level. The second scalar superfield, whose leading component is the physical dilaton field, may be regarded as being external to the superspace geometry. An action for the full non-linear theory is proposed.     

Algebraic approach to supergravity in superspace

The methods of algebraic geometry are used to construct supergravity theories in a homogeneous superspace OSp(N|4) with structure group Sl(2C) ? O_N and base supermanifold the coset space OSp(N|4)/(Sl(2C)? O_N). The nature and origin of the supersymmetry transformations is completely elucidated. The equations of motion for O₁ and O₂ supergravity are obtained, as the realization of this symmetry on the space-time components h_μ of the “supervierbein”.     

A superspace approach to extended conformal supergravity

Extended conformal supergravity is discussed in a superspace context.     

Higher-derivative supergravity in U(l) superspace

The complete structure of curvature squared terms is analyzed in the context of chirally extended supergravity, with special emphasis on the gravitationally induced Fayet–Iliopoulos D–term. Coupling of (chiral) matter is discussed in relation with a possible extension to supergravity of the equivalence mechanism between and General Relativity coupled to a scalar. Received: 9 June 1997 / Revised version: 12 September 1997 / Published online: 26 February 1998     

Definition of superspace in the theory of supergravity

A mathematically rigorous treatment of superspace with even and odd coordinates leads to the appearance of a nilpotent part for even coordinates. Hence, a problem arises in the physical interpretation of the theory of supergravity.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 65–69, April, 1989.     

On-shell and conformal N = 4 supergravity in superspace

We discuss the superspace geometries which are necessary to describe on-shell O(4) and SU(4) supergravity. The relation of central charge field strengths to physical spin-zero fields is exhibited and a “new” O(4) theory is shown to exist. The version of SU(4) supergravity which uses an antisymmetric tensor gauge field is found to require modifications of ordinary superspace. Finally the Poincaré supergeometry which admits the conformal N = 4 supermultiplet is constructed. It is shown that consistency of the Bianchi identities implies the existence of dimension zero auxiliary fields which are components of a non-linear multiplet.     

Some remarks on the geometry of superspace supergravity

In this note, we first give a quick presentation of the supergeometry underlying supergravity theories, using an intrinsic differential geometric language. For this, we adopt the point of view of Cartan geometries, and rely as well on the work of John Lott, who has found a unified geometrical interpretation of the torsion constraints for many supergravity theories, based on the use of H-structures. In this framework, the constraints amount to requiring first-order integrability of H-structures, for a specific supergroup H.The supergroup H used by Lott is not the usual diagonal representation of the Lorentz group on superspace, but an extension of the latter. This extension appears to be natural and it can be related to the super-Poincaré group. We also observe that the constraints arising from the requirement of first-order integrability have basically the same form, in any spacetime dimension.Looking at supergravity from an affine viewpoint (i.e. as a gauge theory for the super-Poincaré group), we show that requiring first-order integrability amounts to requiring the equivalence, up to gauge transformations, between infinitesimal gauge supertranslations acting on the supervielbein and infinitesimal superdiffeomorphisms acting on the supervielbein.The latter action is performed through a covariant Lie derivative, whose expression involves naturally the supertorsion tensor. We use this expression to show that the term added to the spin connection, in the supercovariant derivative of d=11 supergravity, has a natural superspace origin. In particular, the 4-form field strength is related to a specific component of the supertorsion tensor.We conclude by some general remarks concerning Killing spinors in geometry and supergravity, discussing their possible interpretations, as Killing vector fields on a specific supermanifold on one hand, and as parallel spinors for an appropriate connection on the other hand. We show that this last interpretation is very natural from the point of view of Klein and Cartan geometries.     

New D = 10, N = 1 superspace supergravity and local symmetries of superstrings

The superspace formulation of new D = 10, N = 1 supergravity is developed. It is shown that the background superspace of the new theory can be coupled to a test superstring in such a way that the local symmetries of the superstring are intact. This formulation necessarily makes use of the Vainberg construction so the action is analogous to the effective action for QCD with the WZW term. The results suggest that the ambiguity between the massless two-form and six-form in the SO(32) or E₈ × E₈ superstring theories can only be resolved by a gauge invariant, Lorentz-covariant formulation of superstring field theory.     

On-shell O(N) supergravity in superspace

We show that general considerations of the properties of free on-shell O(N) superfield strengths lead directly to linearized on-shell O(N) supergravity. We consequently obtain a formulation of the fully non-linear on-shell theories in which all fields are contained in the covariant derivatives.     

A superspace action for N = 2 supergravity

The action for N = 2 supergravity can be presented as the invariant volume of the chiral subspaces of the real N = 2 superspace. The invariant volume of the real superspace itself is shown to vanish. The real basis form of the action contains covariant Grassmann δ functions involving N = 2 prepotentials explicitly.     

A complete solution of the Bianchi identities in superspace with supergravity constraints

A short discussion of the superspace formulation of supergravity is given and the Bianchi identities are derived. The supergravity constraints are imposed and the identities are solved in terms of superfields and their covariant derivatives.     

Nonlocal action for supertrace anomalies in superspace of N=1 supergravity

We construct the nonlocal quantum effective action generating the supertrace anomaly for the classically superconformal theories in superspace of N=1 supergravity.     

Quotient space solutions of 11-dimensional supergravity

All the Freund-Rubin type solutions of the 11-dimensional supergravity with a simply connected quotient spaceG/H as the compact 7-dimensional manifold are found. Their geometries depend only on the imbedding ofHG and the Riemannian structure ofG/H. In particular, SU₃×SU₂×U₁/SU₂×U₁×U₁, Einstein solutions are discussed in detail.     

Towards a manifestly supersymmetric formulation of N = 8 supergravity on a light-cone superspace

N = 8 supergravity is formulated in the light-cone gauge. An unconstrained superfield defined on a light-cone superspace is constructed from the component formulation. The light-cone superspace is spanned by Grassmann coordinates which belong to the spinor representation of SO(7), a subgroup of the transverse SO(9).