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.     

Formulation of 11-dimensional supergravity in superspace

We formulate on-shell 11-dimensional supergravity in superspace and express its equations of motion in terms of purely geometrical quantities. All torsion and curvature components are solved in terms of a single superfield W_rstu, totally antisymmetric in its (flat vector) indices. The dimensional reduction of this formulation is expected to be related to the superspace formulation of N=8 extended supergravity and might explain the origin of the hidden (local) SU(8) and (global) E₇ symmetries present in this theory.     

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.     

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.     

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.     

Superspace gauge theories with central charges

The superspace constraints leading to off-shell formulations of extended supersymmetric Yang-Mills theories for N = 2 and 4 are generalised to N = 6 in the abelian case. This leads to an on-shell representation of linearized N = 6 supergravity.     

Covariant first and second quantization of the N = 2, D = 10 Brink-Schwarz superparticle

Using a new type of harmonic superspace variables, we reduce the N = 2, D = 10 Brink-Schwarz (BS) superparticle to a system whose constraints are (i) first class, (ii) functionally independent and (iii) Lorentz covariant. We show that these features are essential for a correct covariant quantization. Q_BRST is first rank. By using it to second quantize the system, we obtain a covariant off-shell unconstrained superfield action of the linearized D = 10 type IIB supergravity. A corresponding procedure for the Green Schwarz (GS) superstring is conjectured.     

Nonlocal action for supertrace anomalies in superspace of N=1 supergravity

We construct the nonlocal quantum effective action generating the supertrace anomaly for the classically superconformal theories in superspace of N=1 supergravity.     

Gravitational supervertices in n=1, 4D superstrings

The gravitational supermultiplet for target space-time supersymmetry of four-dimensional heterotic strings is obtained. By an explicit construction of supervertex operators it is shown that the underlying superspace geometry corresponds to the “new-minimal” formulation of N = 1, 4D supergravity. The relation between R-symmetry in target space and the U(1) symmetry of the world-sheet N = 2 superconformal algebra is outlined.     

Gauge boson/Higgs boson unification: The Higgs bosons as superpartners of massive gauge bosons

The N = 4 supergravity theories with local SO(4) invariance are formulated in superspace. The gauged SO(4) theory with two coupling constants (g₁, g₂) is shown to reduce to three inequivalent models: g₁ = g₂ with negative cosmological constant, g₁ = ?g₂ with positive cosmological constant, and g₁ = 0, g₂ ≠ 0 which is a particular case of the Freedman-Schwarz gauged SU(2) ? SU(2) model. The Higgs effect in the vector-scalar sector of the gauged N = 5 supergravity is analyzed.     

New D = 10, N = 1 superspace supergravity and local symmetries of superstrings

The superspace formulation of new D = 10, N = 1 supergravity is developed. It is shown that the background superspace of the new theory can be coupled to a test superstring in such a way that the local symmetries of the superstring are intact. This formulation necessarily makes use of the Vainberg construction so the action is analogous to the effective action for QCD with the WZW term. The results suggest that the ambiguity between the massless two-form and six-form in the SO(32) or E₈ × E₈ superstring theories can only be resolved by a gauge invariant, Lorentz-covariant formulation of superstring field theory.     

Algebraic approach to supergravity in superspace

The methods of algebraic geometry are used to construct supergravity theories in a homogeneous superspace OSp(N|4) with structure group Sl(2C) ? O_N and base supermanifold the coset space OSp(N|4)/(Sl(2C)? O_N). The nature and origin of the supersymmetry transformations is completely elucidated. The equations of motion for O₁ and O₂ supergravity are obtained, as the realization of this symmetry on the space-time components h_μ of the “supervierbein”.     

Vanishing β-functions in extended supergravities

Given that extended supergravity theories can be written in N = 1 superfield form, the non-renormalization of chiral superspace integrals implies a vanishing β-function for the SO(N) gauged Poincaré supergravity theories for N ? 5 at one loop and probably to all orders. In particular, this explains the results of existing one-loop calculations of the β-function.     

The component gauges in supergravity

We present N = 1 supergravity in superspace gauges where the relation to component supergravity is immediate. Among the new results are the inverse vielbein to all orders in φ, some important components of the connection, a Lorentz transformation between our two “component gauges”, the component transformations for a spinor multiplet and some results concerning the axial current for various matter systems coupled to supergravity.     

Superspace formulation ofN=2 supergravity

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

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.     

The complete N =2, d = 10 supergravity

The alternative N = 2, d = 10 supergravity, which is not derivable by dimensional reduction from the N = 1, d = 11 theory, is constructed at the full non-linear level. The transformation laws of the component fields and the equations of motion are derived and shown to be consistent. The derivation makes use of superspace techniques and exploits the fact that the scalars belong to the coset space SU(1,1)/U(1).     

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.     

Superactions

We present a general formalism for constructing super-invariants by integrating over even-dimensional submanifolds of superspace, valid for all N. This result includes all previous action formulae, without central changes, and we use it to derive the on-shell N=4 super-Yang-Mills action and a manifestly SU(8) invariant linearized three-loop counterterm for N=8 supergravity. We also present a compact diagrammatic technique that replaces index manipulation involving spinor derivatives.