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

Understand

We consider Chern-Simons actions of Abelian tensor hierarchy of $p$-form gauge fields in four-dimensional ${\cal N}=1$ 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.