Hypersymmetric extensions of Maxwell-Chern-Simons gravity in 2+1 dimensions

TLDR: In this article, a consistent way of coupling three-dimensional hyper-Maxwell-Chern-Simons gravity theory with massless spin-$\frac{5}{2}$ gauge fields was presented.

Abstract: We present a consistent way of coupling three-dimensional Maxwell-Chern-Simons gravity theory with massless spin-$\frac{5}{2}$ gauge fields. We first introduce the simplest hyper-Maxwell-Chern-Simons gravity generically containing two massless spin-2 fields coupled with a massless Majorana fermion of spin $\frac{5}{2}$ whose novel underlying superalgebra is explicitly constructed. We then present three alternative hypersymmetric extensions of the Maxwell algebra which are shown to emerge from the In\"on\"u-Wigner contraction procedure of precise combinations of the $\mathfrak{o}\mathfrak{s}\mathfrak{p}(1|4)$ and the $\mathfrak{s}\mathfrak{p}(4)$ algebras. This allows us to construct distinct types of hyper-Maxwell-Chern-Simons theories that extend to include generically interacting nonpropagating spin-4 fields accompanied by one or two spin-$\frac{5}{2}$ gauge fields.