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9 papers found.
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N = 1 supercurrents of eleven-dimensional supergravity

Abstract Eleven-dimensional supergravity can be formulated in superspaces locally of the form X × Y where X is 4D N = 1 conformal superspace and Y is an arbitrary 7-manifold admitting a G2-structure. The eleven-dimensional 3-form and the stable 3-form on Y define the lowest component of a gauge superfield on X × Y that is chiral as a superfield on X. This chiral field is part of...

The component structure of conformal supergravity invariants in six dimensions

In the recent paper arXiv:​1606.​02921, the two invariant actions for 6D \( \mathcal{N}=\left(1,0\right) \) conformal supergravity were constructed in superspace, corresponding to the supersymmetrization of C 3 and C□C. In this paper, we provide the translation from superspace to the component formulation of superconformal tensor calculus, and we give the full component actions...

On conformal supergravity and harmonic superspace

This paper describes a fully covariant approach to harmonic superspace. It is based on the conformal superspace description of conformal supergravity and involves extending the supermanifold \( \mathrm{\mathcal{M}} \) 4|8 by the tangent bundle of \( \mathbb{C} \) P 1. The resulting superspace \( \mathrm{\mathcal{M}} \) 4|8 × T \( \mathbb{C} \) P 1 can be identified in a certain...

Eleven-dimensional supergravity in 4D, N = 1 superspace

We give a formulation of linearized 11D supergravity in 4D, N = 1 superspace keeping all eleven bosonic coordinates. The fields are fluctuations around M = R 4|4 × Y, where Y is a background Riemannian 7-manifold admitting a G 2 structure. We embed the 11D fields into superfield representations of the 4D, N = 1 superconformal algebra. These consist of the conformal graviton...

Projective multiplets and hyperkähler cones in conformal supergravity

Projective superspace provides a natural framework for the construction of actions coupling hypermultiplets to conformal supergravity. We review how the off-shell actions are formulated in superspace and then discuss how to eliminate the infinite number of auxiliary fields to produce an on-shell \( \mathcal{N}=2 \) supersymmetric sigma model, with the target space corresponding...

Invariants for minimal conformal supergravity in six dimensions

We develop a new off-shell formulation for six-dimensional conformal super-gravity obtained by gauging the 6D \( \mathcal{N} \) = (1, 0) superconformal algebra in superspace. This formulation is employed to construct two invariants for 6D \( \mathcal{N} \) = (1, 0) conformal super-gravity, which contain C 3 and C□C terms at the component level. Using a conformal supercurrent...

Rigid 4D \( \mathcal{N}=2 \) supersymmetric backgrounds and actions

We classify all \( \mathcal{N}=2 \) rigid supersymmetric backgrounds in four dimensions with both Lorentzian and Euclidean signature that preserve eight real supercharges, up to discrete identifications. Among the backgrounds we find specific warpings of \( {S}^3\times \mathrm{\mathbb{R}} \) and \( {\mathrm{AdS}}_3\times \mathrm{\mathbb{R}} \), AdS2 × S 2 and H 2 × S 2 with...

Conformal supergravity in five dimensions: new approach and applications

We develop a new off-shell formulation for five-dimensional (5D) conformal supergravity obtained by gauging the 5D superconformal algebra in superspace. An important property of the conformal superspace introduced is that it reduces to the super-conformal tensor calculus (formulated in the early 2000’s) upon gauging away a number of superfluous fields. On the other hand, a...

Non-renormalization theorems and N = 2 supersymmetric backgrounds

The conditions for fully supersymmetric backgrounds of general N = 2 locally supersymmetric theories are derived based on the off-shell superconformal multiplet calculus. This enables the derivation of a non-renormalization theorem for a large class of supersymmetric invariants with higher-derivative couplings. The theorem implies that the invariant and its first order variation...