Torsion and curvature in extended supergravity

The first Bianchi identities are used to show, that in extended supergravity the curvature can be expressed in terms of the torsion and its covariant derivatives. The second Bianchi identities are shown to hold on account of the first ones. Thus all expressions containing the curvature may be written in terms of the torsion, which is the fundamental geometric object in supergravity.     

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.     

The axial gauge BRS identities in supergravity

The BRS identities for supergravity in the axial gauge are derived and an identity involving the graviton self energy is verified to one-loop. It is demonstrated that even in a gauge where the anti-symmetric part of the vierbein field does not propagate, it does not decouple from the BRS identities.     

Off-shell BRS-invariant construction of N = 1, D = 4 conformal supergravity

A geometrical construction is displayed of the BRS structure of the N = 1, D = 4 conformal supergravity theory. The requirement of a nilpotent differential structure determines directly the closure of the conformal supergravity transformation laws. All existing geometrical constraints between field strengths are systematically worked out from the requirement of Bianchi identities. As a by-product of the technics involved, some new features of conformal gravity are revealed.     

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.     

On the anti-symmetric vierbein in quantum supergravity

We consider the BRS identities for N = 1 supergravity in a covariant gauge. It is shown that, as in the axial gauge, the anti-symmetric part of the vierbein does contribute to the BRS identities, even though one can choose a gauge in which it does not propagate.     

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.     

A comment on superspace Bianchi identities and six-dimensional spacetime

We investigate the Bianchi identities for a superspace with a six-dimensional spacetime, under the assumption of certain superspace kinematic constraints. It is shown that these constraints lead to the supergravity theory recently discussed by Breitenlohner and Kabelschacht. However, we conclude that the resulting theory is consistent only if the curvature scalar of the six-dimensional spacetime vanishes.     

Anomaly-free supergravity and super-Yang-Mills theories in ten dimensions

We formulate in ten dimensions a supergravity theory coupled to a super-Yang-Mills theory through the Green-Schwarz ansatz, which ensures chiral anomaly cancellation. The formulation is obtained by fixing suitable constraints in the superspace and solving the Bianchi identities. In this way we obtain the whole set of equations of motion. They are characterized by highly non-polynomial expressions, when expressed only in terms of the physical superfields. We discuss the problem of the massive modes appearing in some of these equations.     

Towards a loop representation for quantum canonical supergravity

We study several aspects of the canonical quantization of supergravity in terms of the Ashtekar variables. We cast the theory in terms of a GSU(2) connection and we introduce a loop representation. The solution space is similar to the loop representation of ordinary gravity, the main difference being the form of the Mandelstam identities. Physical states are in general given by knot invariants that are compatible with the GSU(2) Mandelstam identities. There is an explicit solution to all the quantum constraint equations connected with the Chern-Simons form, which coincides exactly with the Dubrovnik version of the Kauffman polynomial. This provides for the first time the possibility of finding explicit analytic expressions for the coefficients of that knot polynomial.     

Basics of M‐theory

This is a review article of eleven dimensional supergravity in which we present all necessary calculations, namely the Noether procedure, the equations of motion (without neglecting the fermions), the Killing spinor equation, as well as some simple and less simple supersymmetric solutions to this theory. All calculations are printed in much detail and with explicit comments as to how they were done. Also contained is a simple approach to Clifford algebras to prepare the grounds for the harder calculations in spin space and Fierz identities.     

Properties of SO(8) extended supergravity

The conjectured SU(8) invariance of the field equations of SO(8) extended supergravity is used to elucidate the general structure of the extended theories. Due to the representation content of the spinless fields this does not lead to a complete determination of the theory, as was the case for N = 4. The non-polynomial modifications by spinless fields are given in terms of a number of SU(8) covariant tensors, for which various identities are derived and discussed.     

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.     

Supergravity,complex geometry andG-structures

The geometry of supergravity is studied. New formulations of supergravity are given. The equivalence of different approaches to supergravity is analyzed.     

Invariance of actions,rheonomy, and the new minimal N = 1 supergravity in the group manifold approach

A new definition of rheonomy is proposed based on Bianchi identities instead of field equation. For theories with auxiliary fields, the transformation rules are obtained in a completely geometrical way and invariance of the action is equivalent to d$\text{P}$ = 0, which means surface-independence of the action integral. For theories without auxiliary fields, the transformation rules are found by requiring that the action be invariant, just as in the component approach. Previous methods of obtaining the transformation rules which start from rheonomy of field equations and use certain recipes to find the off-shell extensions of the rules are abandoned. New minimal supergravity is worked out in detail; it is the gauge theory based on a free differential algebra which includes the auxiliary fields.     

Covariant Field Equations in Supergravity

Covariance is a useful property for handling supergravity theories. In this paper, we prove a covariance property of supergravity field equations: under reasonable conditions, field equations of supergravity are covariant modulo other field equations. We prove that for any supergravity there exist such covariant equations of motion, other than the regular equations of motion, that are equivalent to the latter. The relations that we find between field equations and their covariant form can be used to obtain multiplets of field equations. In practice, the covariant field equations are easily found by simply covariantizing the ordinary field equations.     

The auxiliary field structure in chirally extended supergravity

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.     

The effective action of W 3-gravity

A new method for integrating anomalous Ward identities and finding the effective action is proposed. Two-dimensional supergravity and W ₃-gravity are used as examples to demonstrate its potential. An operator is introduced that associates each physical quantity with a Ward identity, i.e., a quantity that is transformed without anomalous terms and can be nullified in a consistent manner. A covariant form of the action for matter fields interacting with a gravitational and W ₃-gravitational background is proposed. Zh. éksp. Teor. Fiz. 111, 1537–1553 (May 1997)     

Modified interaction of the scalar multiplet coupled to supergravity

It is shown that a modified interaction of the massless scalar multiplet coupled to supergravity can be introduced in a consistent way. For a particular modification, the fermionic quartic terms are those predicted by pure torsion. This modification is precisely the one obtained when the SO(4) extended supergravity theory is reduced to the scalar multiplet coupled to supergravity.