The density multiplet in superspace

We calculate the components of the density multipletE inN=1 superspace and the last component of the chiral density multiplet ? inSU(2) extended superspace with a minimal set of auxiliary fields.     

The vector-tensor multiplet in harmonic superspace

We describe the vector-tensor multiplet and derive its Chern-Simons coupling to the Yang-Mills gauge superfield in harmonic superspace. Received: 10 October 1997 / Published online: 23 February 1998     

The chain rule of differentiation in superspace

The chain rule of differentiation does not hold for superfields. We study precisely the deviation from the usual rule and show that problems stemming from it are tractable in our calculations in superspace.     

Unfolding the singularities in superspace

A method is described for unfolding the singularities in superspace, \(\mathcal{G} = \mathfrak{M}/\mathfrak{D}\) , the space of Riemannian geometries of a manifoldM. This unfolded superspace is described by the projection $$\mathcal{G}_{F\left( M \right)} = \frac{{\mathfrak{M} \times F\left( M \right)}}{\mathfrak{D}} \to \frac{\mathfrak{M}}{\mathfrak{D}} = \mathcal{G}$$ whereF(M) is the frame bundle ofM. The unfolded space \(\mathcal{G}_{F\left( M \right)}\) is infinite-dimensional manifold without singularities. Moreover, as expected, the unfolding of \(\mathcal{G}_{F\left( M \right)}\) at each geometry [g _o] ∈ \(\mathcal{G}\) is parameterized by the isometry groupIg _o (M) of g₀. Our construction is natural, is generally covariant with respect to all coordinate transformations, and gives the necessary information at each geometry to make \(\mathcal{G}\) a manifold. This construction is a canonical and geometric model of a nonrelativistic construction that unfolds superspace by restricting to those coordinate transformations that fix a frame at a point. These particular unfoldings are tied together by an infinite-dimensional fiber bundleE overM, associated with the frame bundleF(M), with standard fiber \(\mathcal{G}_{F\left( M \right)}\) , and with fiber at a point inM being the particular noncanonical unfolding of \(\mathcal{G}\) based at that point. ThusE is the totality of all the particular unfoldings, and so is a grand unfolding of \(\mathcal{G}\) .     

Supertwistors and superspace

In the paper the usual correspondence between twistors and geometrical objects in the Minkowski space is generalized to the supertwistor case by means of flag supermanifolds. This supertwistor correspondence is treated in detail. Chiral and non-chiral superspaces are constructed and their properties studied by means of supertwistors.     

Self-duality in superspace

The absence of local divergences in the vacuum functional of supergravity at all loop orders in a self-dual gravitational or supergravitational background is discussed. It is also shown that the first variational derivative of the generating functional of supergravity has no gauge independent divergences in a self-dual background, in particular that the gauge independent part of the energy momentum tensor is finite in a self-dual background. Simple expressions defining the corresponding half-flat superspace are presented.     

Components of superspace

We give the explicit superspace form of the newly discovered tensor calculus for the chiral multiplet [1].     

Quantum conformal superspace

For a compact connected orientablen-manifoldM, n 3, we study the structure ofclassical superspace ,quantum superspace ,classical conformal superspace , andquantum conformal superspace . The study of the structure of these spaces is motivated by questions involving reduction of the usual canonical Hamiltonian formulation of general relativity to a non-degenerate Hamiltonian formulation, and to questions involving the quantization of the gravitational field. We show that if the degree of symmetry ofM is zero, thenS,S ₀,C, andC ₀ areilh orbifolds. The case of most importance for general relativity is dimensionn=3. In this case, assuming that the extended Poincaré conjecture is true, we show that quantum superspaceS ₀ and quantum conformal superspaceC ₀ are in factilh-manifolds. If, moreover,M is a Haken manifold, then quantum superspace and quantum conformal superspace arecontractible ilh-manifolds. In this case, there are no Gribov ambiguities for the configuration spacesS ₀ andC ₀. Our results are applicable to questions involving the problem of thereduction of Einstein's vacuum equations and to problems involving quantization of the gravitational field. For the problem of reduction, one searches for a way to reduce the canonical Hamiltonian formulation together with its constraint equations to an unconstrained Hamiltonian system on a reduced phase space. For the problem of quantum gravity, the spaceC ₀ will play a natural role in any quantization procedure based on the use of conformal methods and the reduced Hamiltonian formulation.     

Instability in superspace

Using Morse's theory of reconstructions we define the space of all the universes-the Superspace. On the Superspace we investigate the geometry of the DeWitt metric. It is shown that the geodesic flow corresponding to the DeWitt metric is exponentially instable. The dynamical system described by the Einstein equations of evolution (Einstein dynamics) has the same type of instability also, if 1) the Universe is inflationary in some local domain, 2) in some local domain the Universe does not change its volume, but changes the conformal geometry very quickly as compared with the conformal potnetial. So, the Einstein dynamics is unstable on the Superspace, therefore the following quantum theory considered on the minisuperspace (a submanifold of the Superspace with a finite dimension) says nothing about the real quantum theory on the Superspace, and in the Superspace the semiclassical approximation is close to the quantum approximation only during a short time.     

Faddeev-Jackiw quantization in superspace

We consider the constrained Faddeev-Jackiw geometric quantization approach in superspace. We deal with a supersymmetric quantum mechanical model both in components and in superfield language.     

Supergravity geometry in superspace

Recently, Duke and Teper have claimed that the Drell-Yan picture is not applicable in a large kinematic domain where it was applied previously. We point out an error in their arguments, and show that the Drell-Yan model can be applied in a much larger domain.     

Supergravity symmetries in superspace

We show the extension of the Forgacs-Manton Killing symmetry for gauge theories, to solutions, extended to superspace, of the d = 11 supergravity theory.     

Flat superspace with supertorsion

We give a simple proof that a recently suggested theory of space-time as contained in a flat supermanifold with specified torsion in the Fermi variables makes good physical sense. We do this in two parts by showing firstly that supergravity is appropriately contained in such a theory and secondly that the resulting theory, on quantisation, is expected to be renormalisable. We briefly discuss the manner in which matter may be included in this theory.     

Renormalization theory in superspace

The auxiliary mass BPHZ renormalization procedure is extended to include theories defined in superspace. Ultraviolet and infrared power counting formulas for Feynman integrands in superspace are derived. A general momentum-superspace subtraction scheme is given which allows time-ordered Green functions of superfields to be defined as tempered distributions. Superfield normal product Green functions are introduced and the Zimmermann identity relating differently subtracted such products is established. Finally normal product field equations and the renormalized quantum action principle in superspace are derived.     

(2,0) superspace

Superspace formulations of the most general two-dimensional σ models with (2,0) and (2,1) supersymmetry are constructed and some of their implications discussed.