Deconstructing Supergravity: Massive Supermultiplets

Given the success of the deconstruction program in obtaining ghost-free massive gravity from 5-D Einstein gravity, we propose a modification of the deconstruction procedure that incorporates supersymmetry at the linear level. We discuss the relevant limits of a conjectured interacting theory of a massive spin 2 supermultiplet, and determine the linear theory to be the N=1 Zinoviev theory, a supersymmetric extension of Fierz-Pauli theory. We develop a family of 1-site deconstruction procedures for fermionic fields (yielding Dirac and Majorana mass terms). The deconstruction procedure appropriate for giving fermions a Dirac mass is found to preserve half of the supersymmetry of the 5-D theory. We explicitly check this by deconstructing 5-D N=2 super-Maxwell theory down to 4-D N=1 super-Proca theory, and deconstructing linear 5-D N=2 supergravity down to 4-D N=1 Zinoviev theory, and derive the full 4-D supersymmetry algebras and Stueckelberg symmetries from the 5-D superalgebras and gauge symmetries, respectively. We conjecture that this procedure should admit a generalization to fully non-linear theories.