Abelian tensor hierarchy in 4D N $$ \mathcal{N} $$ = 1 conformal supergravity

Abstract

Abstract:We consider Abelian tensor hierarchy in four-dimensional 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. We also show the relation between the superspace formalism and the superconformal tensor calculus.

Abelian tensor hierarchy and Chern-Simons actions in 4D N $$ \mathcal{N} $$ = 1 conformal supergravity

“…The CS actions are constructed by the prepotentials of the p-form gauge superfields in the presence of the tensor hierarchy. 2 We obtain the prepotentials by using so-called covariant approach, which are shown in our previous paper [35]. In the covariant approach, we introduce p-form gauge superfields and their field strength superfields in the superspace.…”

“…[35]. Covariant approach is an approach to constructing supersymmetric theories of p-form gauge fields in superspace.…”

“…[35] except the normalizations of the superfields Y I 3 and L I 2 , which are the same as G S and H M in ref. [16], respectively.…”

“…[35]. The infinitesimal internal gauge transformations δ T (Λ) of the p-form gauge fields are given by…”

“…We remark that the gauge-fixing conditions of p-form gauge fields in table 3 have the same spinor structure as the constraints on the field strengths of (p−1)-form gauge fields in table 2. Thus, we solve the constraints by the same procedure as the Bianchi identities for the field strengths [35]. The conformal weights of the prepotentials…”