Showing papers on "Superspace published in 1987"

$N=2$ Supergravity in Superspace: Different Versions and Matter Couplings

Abstract: This paper concludes the formulation of N=2 supergravity in harmonic superspace. The authors generalize the approach to include conformal supergravity. The superconformal group is then compensated by coupling to a Maxwell and various matter multiplets. All the previously known versions of N=2 Einstein supergravity are reproducible in this way. The authors give one example (with the non-linear multiplet as a compensator). Their main result is a new version of N=2 Einstein supergravity which involves an off-shell complex hypermultiplet with its infinitely many auxiliary fields. They believe this version to be fundamental.

On the structure and symmetry of incommensurate phases. A practical formulation

Abstract: The structural description, symmetry and diffraction properties of incommensurate modulated phases are revised using a real-space framework. The superspace formalism usually employed is reformulated using a practical description where no multidimensional geometrical constructions are needed. The incommensurate structural distortion is described in terms of 'atomic modulation functions' where the internal space is only considered as a continuous label for the cells of the non-distorted structure. Hence, no atomic positions or thermal tensors in a multidimensional space are defined. By this means and with the introduction of the concept of 'atomic modulation factors' a general expression for the structure factor is proposed which constitutes a direct generalization of the standard expression for a commensurate structure. The concept of superspace symmetry is reduced in this approach to a simple relation between the defined atomic modulation functions, which can be directly translated by means of the structure-factor expression into the symmetry and extinction rules of the diffraction diagram. The advantages of superspace formalism in the analysis of commensurate modulated phases are also discussed. The use of superspace groups for describing the symmetry of superstructures, contrary to some recent claims, does not formally reduce the number of structural parameters but may often allow some of them to be neglected.

A superanalog of the Selberg trace formula and multiloop contributions for fermionic strings

Abstract: An analog of the classical Selberg trace formula is given for discrete groups, acting on the upper complex half-superplane. Applications to the fermionic string measure on the moduli superspace are discussed.

N=2 supergravity in superspace: solution to the constraints and the invariant action

Abstract: The authors develop the off-shell unconstrained formulation of N=2 Einstein supergravity in harmonic superspace. The elements of differential geometry are constructed in terms of the prepotentials (the analytic vielbeins of the harmonic covariant derivative D++). Thus, the authors find the solution to the constraints of the first off-shell version of the theory. A number of useful 'building blocks' with simple transformation properties are constructed from the prepotentials. They are used to obtain a density for the full supervolume of harmonic superspace. One can then write down the invariant action for this version of the theory. The proof of the invariance relies on the existence of a new 'hybrid' basis in harmonic superspace in which semi-chirality together with analyticity are manifest.

Anomalies in Two-dimensional Supersymmetric Nonlinear $\sigma$ Models

Abstract: The anomalies of two-dimensional non-linear sigma models are analysed using the Wess-Zumino consistency conditions. In particular, the (2,0) model is discussed in both the (1,0) and (2,0) superfield formalisms. In (1,0) superspace the removal of the holonomy and second supersymmetry anomalies induces a holomorphic holonomy anomaly which agrees with that deduced from the (2,0) superspace consistency conditions. It is shown that the cancellation of the one-loop anomaly by an anomalous variation of an antisymmetric tensor induces no harmful effects at higher loops.

Quantization of classically equivalent theories in superspace of simple supergravity, and quantum equivalence

Abstract: The theories of a chiral spinor superfield and of a real scalar superfield (scalar multiplet), each in an external field of simple supergravity, are considered. Both theories belong to the class of gauge theories with linearly dependent generators. A prescription for quantization is proposed, effective actions are constructed, and the quantum equivalence of these theories to the theory of a nonconformal chiral scalar superfield is demonstrated.

Strings and superspace

Abstract: The scale-invariant superspace formulation of d = 10 Einstein-Yang-Mills system is considered which gives a most economical and clear presentation of the full on-shell content of the theory. Discussion of supersymmetric higher order corrections to the effective action of string theory is based on the corresponding supergeometry. A geometrical formulation of the heterotic string theory in superspace with 10 + 496 bosonic and 16 fermionic coordinates is presented. Minimal constraints on this superspace are found which provide the local fermionic and two types of bosonic world-sheet symmetries of the heterotic string. The relation between this superspace and the anomaly-free d = 10 Einstein-Yang-Mills supergravity is discussed. The existence of a self-dual world-sheet torsion, which is required by the world-sheet symmetries, explains the geometrical origin of the absence of right movers in the gauge degrees of freedom of the heterotic string. The action of the heterotic string in the full curved background has a particularly simple form: .

Structure of N=2 superconformally invariant unitary ``minimal'' theories: Operator algebra and correlation functions

Abstract: N=2 superconformal-invariant theories are studied and their general structure is analyzed. The geometry of N=2 complex superspace is developed as a tool to study the correlation functions of the theories above. The Ward identities of the global N=2 superconformal symmetry are solved, to restrict the form of correlation functions. Advantage is taken of the existence of the degenerate operators to derive the ``fusion'' rules for the unitary minimal systems with c\ifmmode \tilde{}\else \~{}\fi{}1. In particular, the closure of the operator algebra for such systems is shown. The c\ifmmode \tilde{}\else \~{}\fi{}=(1/3 minimal system is analyzed and its two-, three-, and four-point functions as well as its operator algebra are calculated explicitly.

Hyper-Kähler sigma models in extended superspace

Abstract: A self-interaction is constructed for generalized tensor multiplets and the relaxed matter hypermultiplet in N = 2, d = 4 superspace. An explicit formulation is given for a large class of new two-dimensional N = 4 sigma models with hyper-Kaehler metric, and the canceling of all ultraviolet divergences in all orders of perturbation theory is proved for them.

Path-integral formulation of closed strings.

Abstract: We construct the covariant path integral for the Neveu-Schwarz-Ramond superstring in superspace, with manifest invariance under diffeomorphisms and local supersymmetry transformations. Spin structure is introduced, and the constraints imposed by modular invariance on fermionic string models examined. The critical exponents of the bosonic and fermionic string models in space-time dimensions less than the critical dimension are obtained for world surfaces of arbitrary topology.

Supermanifold cohomology and the Wess-Zumino term of the covariant superstring action

Abstract: The cohomology theory of supermanifolds is developed. Its basic properties are established and simple examples given. The Wess-Zumino term in the Green-Schwarz covariant superstring action is interpreted as a nontrivial class in the “supersymmetric cohomology” of flat superspace. A quotient supermanifold with nontrivial topology reflecting this class is constructed. It is shown that there is no topological quantization condition for the coefficient of the Wess-Zumino term. The superstring differs from conventional sigma models in this respect because its action is Grassmann-valued and its group manifold (superspace) is noncompact.

Hyperkähler manifolds and nonlinear supermultiplets

Abstract: We present a new construction of hyperkahler metrics that derives from the 3-dimensionalN=4 nonlinear supermultiplet. Further, we give a detailed description of the nonlinear multiplet inN=2 and 4 superspace.