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We consider Abelian tensor hierarchy in four-dimensional ${cal N}=1$ supergravity in the conformal superspace formalism, where the so-called covariant approach is used to antisymmetric tensor fields. We introduce $p$-form gauge superfields as superforms in the conformal superspace. We solve the Bianchi identities under the constraints for the superforms. As a result, each of form fields is expressed by a single gauge invariant superfield. The action of superforms is shown with the invariant superfields. We also show the relation between the superspace formalism and the superconformal tensor calculus.
We solve the Wess-Zumino consistency conditions of $mathcal{N}=1$ off-shell conformal supergravity in four dimensions and determine the general form of the superconformal anomalies for arbitrary $a$ and $c$ anomaly coefficients to leading non trivial
We suggest three new ${cal N}=1$ conformal dual pairs. First, we argue that the ${cal N}=2$ $E_6$ Minahan-Nemeschansky (MN) theory with a $USp(4)$ subgroup of the $E_6$ global symmetry conformally gauged with an ${cal N}=1$ vector multiplet and certa
This paper presents a projective superspace formulation for 4D N = 2 matter-coupled supergravity. We first describe a variant superspace realization for the N = 2 Weyl multiplet. It differs from that proposed by Howe in 1982 by the choice of the stru
The superspace formulation of N=1 conformal supergravity in four dimensions is demonstrated to be equivalent to the conventional component field approach based on the superconformal tensor calculus. The detailed correspondence between two approaches
We describe the supersymmetric completion of several curvature-squared invariants for ${cal N}=(1,0)$ supergravity in six dimensions. The construction of the invariants is based on a close interplay between superconformal tensor calculus and recently