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

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.