Five-dimensional Supergravity in N = 1/2 Superspace

TL;DR

This paper develops a five-dimensional N=1 supergravity framework within a four-dimensional superspace, making some supersymmetries manifest and enabling the construction of specific invariants relevant to theoretical physics.

Contribution

It introduces a novel 5D, N=1 supergravity formalism in 4D superspace with an extra bosonic coordinate, facilitating new invariant constructions.

Findings

Constructed 5D, N=1 supergravity in 4D superspace.

Reduced to known superspace results in linearized limit.

Built the  \uwedge R \uwedge R invariant within this formalism.

Abstract

We construct 5D, N = 1 supergravity in a 4D, N = 1 superspace with an extra bosonic coordinate. This represents four of the supersymmetries and the associated Poincar\'e symmetries manifestly. The remaining four supersymmetries and the rest of the Poincar\'e symmetries are represented linearly but not manifestly. In the linearized approximation, the action reduces to the known superspace result. As an application of the formalism, we construct the $\int A\wedge R\wedge R$ invariant in this superspace.