Superspace first order formalism, trivial symmetries and electromagnetic interactions of linearized supergravity

A bstract We introduce a first order description of linearized non-minimal ( n = − 1) supergravity in superspace, using the unconstrained prepotential superfield instead of the conventionally constrained super one forms. In this description, after integrating out the connection-like auxiliary superfield of first-order formalism, the superspace action is expressed in terms of a single superfield which combines the prepotential and compensator superfields. We use this description to construct the supersymmetric cubic interaction vertex 3 / 2 − 3 / 2 − 1 / 2 which describes the electromagnetic interaction between two non-minimal supergravity multiplets (superspin Y = 3 / 2 which contains a spin 2 and a spin 3/2 particles) and a vector multiplet (superspin Y = 1 / 2 contains a spin 1 and a spin 1/2 particles). Exploring the trivial symmetries emerging between the two Y = 3 / 2 supermultiplets, we show that this cubic vertex must depend on the vector multiplet superfield strength. This result generalize previous results for non-supersymmetric electromagnetic interactions of spin 2 particles. The constructed cubic interaction generates non-trivial deformations of the gauge transformations.