Superspace unmasked: The physical interpretation of supergravity theory

Supergravity admits a geometric formulation in terms of an expanded algebra of functions on ordinary spacetime. This formulation, called graded manifold theory, is equivalent to the usual superspace supergravity constructions but avoids the anticommuting coordinates of superspace. The geometry suggests an operational interpretation of supergravity theory in terms of measurements made by local observers in spacetime.     

Superspace geometry and N = 1 non-minimal supergravity

We investigate superspace geometry for supergravity with non-minimal auxilliary fields. We find that the kinematic constraints and the superspace Bianchi identities are sufficient to obtain complete component expansions of all superspace quantities, including the vielbein and connection superfields. We include a detailed pedagogical discussion on the analysis of constrained superspace Bianchi identities, demonstrating how these are used to derive component field content and transformation laws. We also note that local, chiral supersymmetry representations which form arbitrary representations of the Lorentz group can exist only within the context of supergravity with non-minimal auxilliary fields.     

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.     

Geometry ofN=1 supergravity (II)

The supergravity torsion and curvature constraints are shown to be a particular case of constraints arising in a general geometrical situation. For this purpose, a theorem is proved which describes the necessary and sufficient conditions that the given geometry can be realized on a surface as one induced by the geometry of the ambient space. The proof uses the theory of nonlinear partial differential equations in superspace, Spencer cohomologies, etc. This theorem generalizes various theorems, well known in mathematics (e.g., the Gauss—Codazzi theorem), and may be of its own interest.     

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.     

Superfields,auxilliary fields and tensor calculus for N=2 extended supergravity

Starting from the geometry of superspace, we find constraints for torsion and curvatures, which lead to off-shell realizations of N=2 supergravity. We give the action formula, and construct the supergravity lagrangian from it.     

On 2D <Emphasis Type="Italic">N</Emphasis> = (4,4) superspace supergravity

We review some recent results obtained in studying superspa.ee formulations of 2D N = (4,4) matter-coupled supergravity. For a superspace geometry described by the minimal supergravity multiplet, we first describe how to reduce to components the chiral integral by using “ectoplasm” superform techniques as in arXiv:0907.5264 and then we review the bi-projective superspace formalism introduced in arXiv:0911.2546. After that, we elaborate on the curved bi-projective formalism providing a new result: the solution of the covariant type-I twisted multiplet constraints in terms of a weight-(−1, −1) bi-projective superfield.     

A dual formulation of supergravity-matter theories

Generating supersymmetric AdS solutions in non-minimal supergravity in four dimensions is notoriously difficult. Indeed, it is a longstanding lore that such solutions exist only for old minimal supergravity. In this paper, we construct a dual formulation for general N=1 supergravity-matter systems that avoids the problem. In the case of pure supergravity without a cosmological constant, it coincides with the usual non-minimal (n=−1) supergravity, but in the presence of matter (or a cosmological constant) our formulation differs considerably. We also elaborate upon the framework of conformal superspace and the compensator method as applied to our theory. In particular, we show that one can encode the details of the Kähler potential and superpotential entirely within the geometry of superspace so that the general sigma-model action is encoded in a single compact term: the supervolume. Finally, we discuss the issue of supercurrents and propose a general form for the supercurrent in AdS.     

Torsion constraints in supergeometry

We derive the torsion constraints for superspace versions of supergravity theories by means of the theory ofG-structures. We also discuss superconformal geometry and superKähler geometry.Permanent address as of September 1, 1990: Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA     

Superspace formulation of supergravity

The recent superspace formulations of supergravity using vierbeins are shown to be equivalent to the previous metric tensor superspace formulation of the authors for physical (mass-shell) spaces. An alternate method of gauge completing the vierbein without using Breitenlohner fields is given to the order necessary to generate field equations, and again shown dynamically equivalent to the above formulations.     

Superspace formulation ofN=2 supergravity

A complete formulation ofN=2 supergravity in superspace is given including a superfield lagrangian.     

Manifestly supersymmetric O(α′) superstring corrections in new D = 10, N = 1 supergravity Yang-Mills theory

A systematic procedure in superspace to derive the O(α′) tree-level superstring corrections to the new D = 10, N = 1 (dual) supergravity Yang-Mills system is established. All the tree-level O(α′) corrections in the closed supersymmetry transformation laws are presented explicitly. These O(α′) corrections are regarded as a generalization of “matter” couplings in D = 10, N = 1 supergravity. The advantage of the superspace approach, based on superspace Bianchi identities, in comparison with the component formulation is elucidated. This new method is applicable to all anomaly-free D ⩽ 10 non-maximal supergravity theories, which utilize the Green-Schwarz mechanism. It also provides a way of introducing general higher-order powers of curvature tensors in D ⩽ 10 supergravity theories.     

Prepotentials in superstring world sheet supergravity

The vielbein of (p, 0) supergravity is solved for in terms of prepotentials. The properties of the prepotentials under supercoordinate, Lorentz, and super-Weyl transformations are discussed, and a proof given that (p, 0) superspace is superconformally flat. The superdeterminant of the (p, 0) supergravity vielbein is shown to transform as a density superfield. Using this density, the Einstein and heterotic string actions are constructed in an arbitrary gauge, and proven to be invariant under super-Weyl transformations.     

The structure of the new superspace

The new superspace of Wess and Zumino is generalized to the unconstrainedN-extendedD-dimensional case, it amounts actually to a reparametrization of the old superspace. Recurrence relations for the transformation law and for the covariant derivatives of the superfields defined in the new superspace are obtained. The definition of the component fields as local Lorentz covariant fields has the consequence that the gauge covariant expressions obtained for the vielbein and the connection of the new superspace don't contain the terms dropped out in the Wess-Zumino gauge of supergravity.     

BRS algebras of Poincaré and conformal supergravity

Starting from the geometric BRS differential algebra in superspace, we elucidate a recently given method [1] for deriving the BRS component field algebras of Poincaré supergravity and we extend this formalism to conformai supergravity. For the latter, the general procedure is illustrated in detail by the two-dimensional (1, 0) theory. In conclusion, we explicitly check the consistency of the whole approach and apply it to verify the WZ integrability condition for the (1, 0) superconformai anomaly.     

Simple 10-dimensional supergravity in superspace

Differential geometry is used to formulate supergravity in a 10-dimensional superspace. From the knowledge of the supersymmetric set of fields in x-space we derive the constraints on the supertorsion and on a super 3-form field strength. We then solve the equations which follow from the Bianchi identities. The solution obtained, which is on the mass shell, is shown to be completely described in terms of a scalar superfield.     

Off-shell d=10, N=1 Poincaré supergravity and the embeddibility of higher-derivative field theories in superspace

The constraints on the supertorsion are presented which lead to off-shell d=10, N=2 Poincaré supergravity and the superfluids which are known to enter the superspace action are identified. It is pointed out that Poincaré off-shell constraints have to be used in a superspace formulation of the low-energy effective actions of N=1 superstrings. However, current formulations of N=1 superstrings propagating in arbitrary supergravity backgrounds are incompatible with these off-shell constraints.     

Natural constraints for extended superspace

A simple systematic method to derive superspace constraints is presented. Constraints are given for extended supergravity with one- and two-form gauge potentials in four space-time dimensions. The natural constraints lead to equations of motion forN>4 (supergravity), resp.N>2 (gauge potentials). We discuss modifications for higherN. We also discuss modifications of the field strength of the two-form potential to include Chern-Simons three-forms.     

Manifestly supersymmetric extensions of (curvature)2-terms in six-dimensional N = 2 supergravity

A systematic and manifestly supersymmetric procedure for supersymmetrization of general (curvature)²-terms in N = 2 supergravity in six dimensions (D = 6) is presented in superspace. The general form of new terms for the supersymmetrization in supertranslation rules is given. As a by-product, the superspace structure of quaternionic Kähler manifolds is elucidated. Our method is the D = 6 application of our previously established formulation for the D = 10, N = 1 supergravity with the O(α′) superstring corrections.