Resonant superalgebras and $\mathcal{N}=1$ supergravity theories in three spacetime dimensions

TL;DR

This paper introduces new supersymmetric extensions of resonant algebras in three dimensions, providing a systematic algebraic framework that links various supergravity and Chern-Simons actions.

Contribution

It presents novel superalgebras with one fermionic charge and an additional bosonic generator, expanding the algebraic structures used in supergravity theories.

Findings

Eight new supersymmetric JPZ+Q schemes derived from super-Jacobi identities

Framework clarifies relations between different supergravity and Chern-Simons actions

Conditions identified for superalgebras to be incorporated into supergravity actions

Abstract

We explore $\mathcal{N}=1$ supersymmetric extensions of algebras going beyond the Poincar\'e and AdS ones in three spacetime dimensions. Besides reproducing two known examples, we present new superalgebras, which all correspond to supersymmetric extensions with one fermionic charge $Q_{\alpha}$ concerning the so-called resonant algebras being characterized by the presence of an additional bosonic generator $Z_{a}$, besides the Lorentz $J_{a}$ and translation $P_{a}$ generators. Obtained eight supersymmetric $JPZ+Q$ schemes result directly from obeying super-Jacobi identities. We point out particular requirements that superalgebras have to satisfy to be successfully incorporated within valid supergravity actions. The presented algebraic and Lagrangian framework organizes and helps us better understand relations between the various supergravity and supersymmetric Chern-Simons actions invariant under diverse resonant superalgebras.