$\mathcal{N}$-extended Maxwell supergravities as Chern-Simons theories in three spacetime dimensions

Abstract

We present a new class of three-dimensional $\mathcal{N}$-extended supergravity theories based on the $\mathcal{N}$-extended Maxwell superalgebra with central charges and $\mathfrak{so}(\mathcal{N})$ internal symmetry generators. The presence of $\mathfrak{so}(\mathcal{N})$ generators is required in order to define a non-degenerate invariant inner product. Such symmetry allows us to construct an alternative supergravity action without cosmological constant term. Interestingly, the new theories can be obtained as a flat limit of a $\mathcal{N}$-extended AdS-Lorentz supergravity theories enlarged with $\mathfrak{so}(\mathcal{N})$ gauge fields.