Off-shell Supergravity Research Articles

Minimal off-shell supergravity in five dimensions

We give an off-shell formulation of N=2 Poincaré supergravity in five dimensions.

(4,4) supergravity and (4,4) super-Liouville action in superspace

We present the N=4 superspace constraints for the two-dimensional (2d) off-shell (4,4) supergravity with the superfield strengths expressed in terms of a (4,4) twisted (scalar) multiplet TM-I in a form suitable for applications. The constraints are shown to be invariant under the N=4 super-Weyl transformations, whose N=4 superfield parameters form another twisted (scalar) multiplet TM-II. The full (4,4) superconformally invariant (improved) TM-II matter action is found. The latter can be extended to the fully covariant and (4,4) locally supersymmetric Liouville action which is suitable for describing (4,4) supersymmetric non-critical strings.

(4,4) superfield supergravity

We present the N = 4 superspace constraints for the two-dimensional off-shell (4,4) supergravity with the superfield strengths expressed in terms of a (4,4) twisted (scalar) multiplet TM-I, as well as the corresponding component results, in a form suitable for applications. The constraints are shown to be invariant under the N = 4 super-Weyl transformations, whose N = 4 superfield parameters form another twisted (scalar) multiplet TM-II. To solve the constraints, we propose an ansatz which makes the N = 4 superconformal flatness of the N = 4 supergravity curved superspace manifest. Locally (4,4) supersymmetric TM-I matter couplings are constructed, with potential terms resulting from spontaneous supersymmetry breaking. We also find the full (4,4) superconformally invariant (improved) TM-II matter action. The latter can be extended to the (4,4) locally supersymmetric Liouville action which is suitable for describing (4,4) supersymmetric non-critical strings.

Toward an off-shell 11D supergravity limit of M-theory

We demonstrate that in addition to the usual fourth-rank superfield ( W abcd ) which describes the on-shell theory, a spinor superfield ( J α ) can be introduced into the 11D geometrical tensors with engineering dimensions less or equal to one in such a way to satisfy the Bianchi identities in superspace. The components arising from J α are identified as some of the auxiliary fields required for a full off-shell formulation. Our result indicates that eleven-dimensional supergravity does not have to be completely on-shell. The κ-symmetry of the supermembrane action in the presence of our partial off-shell supergravity background is also confirmed. Our modifications to eleven-dimensional supergravity theory are thus likely relevant for M-theory. We suggest our proposal as a significant systematic off-shell generalization of eleven-dimensional supergrravity theory.

EXTENDED CONFORMAL SUPERGRAVITY AND BELTRAMI VARIABLES

By using a geometric BRST formalism we investigate the two-dimensional N = 2 and N = 4 superspace geometry. The BRST algebra allows one to generalize the notion of Beltrami variables to the extended supergeometries. Furthermore, this geometric treatment yields a systematic way to derive different off-shell supergravities. Finally we construct the Chern–Simons form and calculate from this the superconformal anomaly for the N = 2 and N = 4 theories.

5-brane effective field theory on Calabi--Yau 3-folds

We consider the compactification of the dual form of N=1, D=10 supergravity on a six-dimensional Calabi--Yau manifold. An N=1 off-shell supergravity effective Lagrangian in four dimensions can be constructed in a dual version of the gravitational sector (new-minimal supergravity form). Superspace duality has a simple interpretation in terms of Poincaré duality of two-form cohomology. The resulting 4D Lagrangian may describe the low-energy point-field limit of a five-brane theory, dual to string theory, provided Calabi--Yau spaces are consistent vacua of such dual theory.

N = 2 chiral bosons in superspace : Stefano Bellucci. INFN-Laboratori Nazionali di Frascati, P.O. Box 13, I-00044 Frascati, Italy; and Evgenyi Ivanov and Sergey Krivonos. JINR-Laboratory of Theoretical Physics, Dubna, Head Post Office, P.O. Box 79, 101 000 Moscow, Russia

We present the N=4 superspace constraints for the two-dimensional (2d) off-shell (4,4) supergravity with the superfield strengths expressed in terms of a (4,4) twisted (scalar) multiplet TM-I in a form suitable for applications. The constraints are shown to be invariant under the N=4 super-Weyl transformations, whose N=4 superfield parameters form another twisted (scalar) multiplet TM-II. The full (4,4) superconformally invariant (improved) TM-II matter action is found. The latter can be extended to the fully covariant and (4,4) locally supersymmetric Liouville action which is suitable for describing (4,4) supersymmetric non-critical strings.

The d = 4, N = 1 supergravity multiplet of the heterotic string

We construct a new auxiliary antisymmetric tensor vertex operator for the heterotic string in d = 4 space-time preserving N = 1 supersymmetry, thus extending the supergravity vertex operator multiplet found previously. We, then, obtain the supersymmetry transformations of the background fields associated with these vertex operators and find them to be the same as those of the component fields of the new minimal supergravity multiplet and a physical linear multiplet coupled to new minimal supergravity. We show that it is not possible to obtain other off-shell supergravity multiplets from string theory and, hence, conclude that the heterotic string in d = 4 space-time gives new minimal supergravity.

Off-shell six-dimensional supergravity in harmonic superspace

A fully off-shell action for N=2, d=6 Poincare supergravity in harmonic superspace is proposed. It consists of the off-shell actions for a scalar multiplet and for a self-dual tensor multiplet in conformal supergravity background. A new mechanism for describing self-dual tensor fields off shell, in which conformal supergravity plays an active role, is found.

Minimal N = 2 off-shell supergravity

It is shown that the standard N = 2 supergravity multiplet (40 + 40) is reducible to a minimal multiplet with 32 bosonic and 32 fermionic degrees of freedom. The latter contains one graviton, two gravitinos, one photon, a N = 2 hypermultiplet, and three auxiliary fields. Three of the four scalars of the hypermultiplet are described off-shell by antisymmetric tensors.

'N=1, D=6' supergravity theory

The superspace torsions constraints are imposed and a solution of the Bianchi identities in terms of superfields and their covariant derivatives is given. The author shows the component fields and exhibit a Lagrangian which couples on-shell supergravity and a matter multiplet. Finally it is shown that after dimensional reduction the N=1, D=6 off-shell supergravity theory yields the N=2, D=4 off-shell conformal supergravity theory.

Nonpolynomiality, prepotentials and superspace geometry

After an introductory discussion of auxiliary fields in supersymmetric theories, we discuss the off-shell structure of N ⩽ 4 supergravity; presenting superspace prepotentials and gauge groups. Evidence is shown that suggests nonlinearity must play an essential role for N 4 off-shell supergravity theories.

Off-shell no-go theorems for higher dimensional supersymmetries and supergravities

By a simple fermion counting argument we show in which space-time dimensions the existence of off-shell supersymmetric Yang-Mills and supergravity theories with an off-shell supersymmetry algebra without “central charges” are allowed. In particular we show that the maximally extended theories require “central charges” or lose explicit Lorentz covariance (as in the light-cone gauge), and that for N ⩾ 3, d = 4 only N = 4 supergravity coupled to six Yang-Mills multiplets can avoid the theorems and the off-shell algebra may not have “central charges”.

Supergravity in superspace

A comprehensive discussion of the formulation of supergravity theories in superspace is presented. After reviewing the general formalism and the linearized theory, we exhibit a complete solution to the Bianchi identities for all N. This solution still contains a reducible representation of supersymmetry and further constraints are imposed to obtain off-shell conformal supergravity ( N ⩽ 4). N = 1 and 2 off-shell Poincaré supergravities are rederived from the corresponding conformal theories. On-shell Poincaré supergravity is discussed for all N in superspaces with additional bosonic coordinates.