Abelian tensor hierarchy and Chern-Simons actions in 4D N=1 conformal supergravity

Abstract

We consider Chern-Simons actions of Abelian tensor hierarchy of $p$-form gauge fields in four-dimensional $\mathcal{N}=1$ supergravity. Using conformal superspace formalism, we solve the constraints on the field strengths of the $p$-form gauge superfields in the presence of the tensor hierarchy. The solutions are expressed by the prepotentials of the $p$-form gauge superfields. We show the internal and superconformal transformation laws of the prepotentials. The descent formalism for the Chern-Simons actions is exhibited.

19 pages

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• Couplings of N=1 chiral spinor multiplets