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

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 containing two massless spin-2 fields coupled with a massless Majorana fermion of spin-$\frac{5}{2}$ and whose novel underlying superalgebra is explicitly constructed. Then, we 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 $\mathfrak{o}\mathfrak{s}\mathfrak{p}\left(1\mathrm{\mid }4\right)$ and the $\mathfrak{s}\mathfrak{p}\left(4\right)$ algebras. This allow us to construct distinct types of hyper-Maxwell Chern-Simons theories that extend to include generically interacting non-propagating spin-$4$ fields accompanied by one or two spin-$\frac{5}{2}$ gauge fields.