Superstrings and the auxiliary field structure of supergravity

We construct the complete superfield of vertex operators corresponding to the four-dimensional N = 1 supergravity multiplet associated with the heterotic superstring. The supergravity fields are shown to consist of a graviton, gravitino, and two auxiliary fields and to form a new minimal supermultiplet. The role of R-invariance in new minimal supergravity is discussed.     

Stability in gauged extended supergravity

Extended supergravity theories with gauged SO(N) internal symmetry have, for N ≥ 4, scalar field potentials which are unbounded below. Nevertheless, it is argued that the theories have ground states with anti-de Sitter background geometry which are stable against fluctuations which vanish sufficiently fast at spatial infinity. Stability is implied because the appropriate conserved energy functional is positive for such fluctuations. Anti-de Sitter space is not globally hyperbolic, but the boundary conditions required for positive energy are also shown to give free field theories with well-defined Cauchy problem. New information on the particle representations of OSp(1, 4) supersymmetry is presented as part of the argument. Supersymmetry requires boundary conditions for spin 0 fields such that only the improved stress tensor leads to a conserved energy functional. Although the stability arguments support the view that gauged supergravity theories are acceptable quantum field theories, the problem of a large cosmological term in the Ads phase of the theories is still unsolved.     

On the auxiliary fields of supergravity

The relation between two sets of auxiliary fields for supergravity, i.e. the Lie algebra valued vector multiplet in the Wess-Zumino gauge and the minimal set with 6 auxiliary fields is exhibited. This gives rise to a formulation with a gauge multiplet for the chiral transformations.     

Heterotic superstrings in auxiliary field background and extended spacetime supersymmetry

We introduce the superstring vertices of the auxiliary connections of extended supergravity and elucidate the relation between the internal symmetry of the spacetime superconformal algebra and the Kac-Moody symmetry of the 2D superconformal algebra. The microscopic computation of effective lagrangians is outlined: it turns out that the low-energy effective lagrangians for 4D heterotic superstrings are of a standard supergravity form.     

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.     

Gauge internal symmetry in extended supergravity

Extended supergravity theories with global O(2) and SO(3) internal symmetry have recently been constructed, and a mechanism which implements local O(2) and SO(3) gauge invariance is given here. The introduction of a minimal gauge coupling automatically leads to a $\text{spin}\text{-}\text{3}\text{2}$ mass and a cosmological term in order to preserve local supersymmetry. Local internal symmetry for a $\text{spin}\text{-}\text{3}\text{2}$ field is related to spontaneous breakdown of global supersymmetry. Perturbation theory results which confirm the physical consistency of the system are given.     

Higher order invariants in extended supergravity

On-shell linearized extended supergravity is presented in superspace for all N. The formalism is then used in the construction of higher order invariants which may serve as counterterm lagrangians. It is shown that three-loop counterterms exist for N ? 3 and (N ? 1)-loop counterterms for N ? 4. In the full non-linear theory, the presence of a global non-compact symmetry group for N ? 4 does not allow a simple extension of the (N ? 1)-loop term, but N-loop counterterms may be constructed.     

Geometrical interpretation of extended supergravity

SO₂ extended supergravity is shown to be a geometrical theory, whose underlying gauge group is OSp(4, 2). The couplings which gauge the SO₂ symmetry as well as the accompanying cosmological and masslike terms are directly obtained, and the usual SO₂ model is obtained after a Wigner-Inönü group contraction.     

Three-loop counterterms for extended supergravity

An invariant three-loop counterterm is exhibited for O(2) supergravity; its presence would imply nonrenormalizability. The analogous one-loop invariant due to O(2) supermatter coupling is also given. Involved are new conserved quantities due to the internal symmetry and to symmetry between fields separated by one spin unit.     

Off-shell extended supergravity and central charges

We discuss the problem of field redefinition for irreducible representations of N = 3 and 4 supersymmetry in order that they reduce on-shell to the corresponding supergravities. We find that such redefinition is impossible in the Fermi sector in these cases. We conclude that central charges are essential to achieve such reduction, and that in particular they must be spin-reducing.     

Algebraic properties of extended supergravity theories

Chirality transformations and generalized duality transformations are used to show that the extended O(2) and O(3) supergravity theories in fact have a U(2) and a U(3) invariance respectively. The coupling of these supergravity theories to matter multiplets having global extended supersymmetry is considered. In one case where the matter multiplet has a non-vanishing central charge, one finds a minimal coupling of the vector field of the supergravity multiplet.     

A superspace approach to extended conformal supergravity

Extended conformal supergravity is discussed in a superspace context.     

Relation between different auxiliary field formulations of N = 1 supergravity coupled to matter

We establish the connection between the old minimal set of auxiliary fields, the new minimal set and the Breitenlohner set. We show that the class of interactions which can be described by the latter two sets are particular cases of the interactions described in the old minimal set. The old and new minimal sets of auxiliary fields are equivalent for R-symmetric lagrangians. The precise correspondence of the bosonic part of the lagrangians in the two minimal formulations is exhibited. In particular, this equivalence shows that one can have both a Fayet-Iliopoulos term and spontaneously broken supersymmetry with vanishing cosmological constant.     

Infinite symmetry algebras of extended supergravity theories

When extended supergravity theories with noncompact symmetry groups are written in a physical gauge, the noncompact symmetries join with the supersymmetries to generate an infinite-dimensional algebra. The details are worked out explicitly for a two-dimensional theory with an SU(1, 1) internal symmetry. Our analysis confirms the observation of Ellis et al. that the infinite rigid superalgebra should be obtained from the finite-dimensional local superalgebra by replacing scalar fields with their asymptotic values at infinity. The infinite algebra is described by extending the super-Poincaré generators to functions on the coset space defined by the scalar fields at infinity. While mathematically nontrivial, this result is, in a certain sense, trivial from a physical point of view.     

Algebraic properties of extended supergravity in DE sitter space

General features of extended supergravity with a gauge internal symmetry are discussed from a group-theoretical point of view.     

On the sigma-model structure of type IIA supergravity action in doubled field approach

In this letter, we describe how to string together the doubled field approach by Cremmer, Julia, Lü, and Pope with the Pasti-Sorokin-Tonin technique to construct the sigma-model-like action for type IIA supergravity. The relation of the results with those obtained in the context of searching for superstring/M-theory hidden symmetry group is discussed.     

Geometrization in the Yang-Mills extended supergravity and Klein-Kaluza versions

We relate personal encounters of three kinds with geometrical approaches, in the development of a relativistic quantum field theory of the fundamental interactions—including interactions with Nathan Rosen. We characterize the geometrical structures involved and discuss the more recent attempts to develop a unified theory based on a Klein-Kaluza contraction of the eightfold extended supergravity.Invited paper, dedicated to Nathan Rosen on the occasion of his seventy-fifth birthday.On leave from Tel Aviv University, Israel, and the University of Texas at Austin, Texas.     

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.     

The structure ofN=16 supergravity in two dimensions

We extend the previously constructed linear system forN=16 supergravity in two dimensions by including the unphysical gravitino degrees of freedom. This theory has a residualN=16 superconformal invariance that can be bosonized to localE ₉ transformations. The modifications to the linear system described here suggest a further extension to an infinite hierarchy of fields and associated gauge transformations related toE ₉.On leave of absence from: Department of Mathematics, Massachusetts Institute of Technology, Cambridge MA 02139, USAWork supported in part by National Science Foundation Grant #85-07109