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

TL;DR

This paper develops new hypersymmetric extensions of Maxwell Chern-Simons gravity in 2+1 dimensions, introducing novel superalgebras and constructing theories with interacting higher-spin fields, including spin-4 and spin-5/2 gauge fields.

Contribution

It introduces three new hypersymmetric extensions of the Maxwell algebra derived via Inönü-Wigner contraction, leading to novel hyper-Maxwell Chern-Simons theories with higher-spin interactions.

Findings

Constructed explicit superalgebras for hypersymmetric extensions.

Developed three distinct hyper-Maxwell Chern-Simons theories.

Included non-propagating spin-4 and spin-5/2 gauge fields.

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 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 $\mathfrak{osp}\left(1|4\right)$ and the $\mathfrak{sp}\left(4\right)$ 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.