$\mathcal{N}=2$ resonant superalgebra for supergravity

TL;DR

This paper introduces a new $ ext{N}=2$ superalgebra for 3D and 4D supergravity with a $U(1)$ generator, based on the Soroka-Soroka algebra, and constructs a Chern-Simons supergravity model.

Contribution

It presents the first explicit realization of an $ ext{N}=2$ superalgebra with a $U(1)$ generator rooted in the Soroka-Soroka algebra and develops a corresponding 3D Chern-Simons supergravity theory.

Findings

New superalgebra with $U(1)$ generator for $ ext{N}=2$ supergravity.

Construction of a 3D Chern-Simons supergravity model based on this algebra.

Discussion of the superalgebra's relevance to supergravity theories.

Abstract

We present new superalgebra for $\mathcal{N}=2$ $D=3,4$ supergravity theory endowed with the $U(1)$ generator. The superalgebra is rooted in the so-called Soroka-Soroka algebra and spanned by the Lorentz $J_{ab}$ and Lorentz-like $Z_{ab}$, translation $P_a$ and $T$ generators, as well as two supercharges $Q^I_\alpha$. It is the only possible realization for a given generator content. We construct a corresponding 3D Chern-Simons supergravity realization of the superalgebra and discuss its relevance.