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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...

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...

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...

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 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...

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...

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...

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...

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...