Holst-MacDowell-Mansouri action for (extended) supergravity with boundaries and super Chern-Simons theory

A bstract In this article, the Cartan geometric approach toward (extended) supergravity in presence of boundaries will be discussed. particular, based on new developments field, we derive Holst variant MacDowell-Mansouri action for $$ \mathcal{N} N = 1 and 2 pure AdS D 4 arbitrary Barbero-Immirzi parameters. This turns out to play a crucial role context framework if one imposes supersymmetry invariance at boundary. For case, it follows that amounts introduction ? -topological term Yang-Mills sector which explicitly depends parameter. shows close connection between parameter -ambiguity gauge theory. We also discuss chiral limit theory, possess some very special properties such as manifest resulting under an enlarged symmetry. Moreover, show demanding boundary yields unique corresponding super Chern-Simons theory with OSp( |2) group. context, conditions couple bulk degrees freedom equivalence results found D’Auria-Fré non-chiral These provide step towards quantum description supersymmetric black holes loop gravity.