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.
Highlights
Hypergravity was an early alternative to supergravity theory [1,2] proposed by Aragone and Deser [3] that deems a spin-5=2 field as the superpartner of the graviton
In what follows we address this question by considering a nontrivial extension of the Poincarealgebra that has long been known as the Maxwell algebra [28,29], which is associated with the symmetry group of the Dirac (Klein-Gordon) equation minimally coupled to a constant electromagnetic field in Minkowski space in 3 þ 1 dimensions [30]
We have presented a consistent way of coupling three-dimensional Maxwell-CS gravity theory with a spin-52 gauge field
Summary
Hypergravity was an early alternative to supergravity theory [1,2] proposed by Aragone and Deser [3] that deems a spin-5=2 field as the superpartner of the graviton. In what follows we address this question by considering a nontrivial extension of the Poincarealgebra that has long been known as the Maxwell algebra [28,29], which is associated with the symmetry group of the Dirac (Klein-Gordon) equation minimally coupled to a constant electromagnetic field in Minkowski space in 3 þ 1 dimensions [30]. We show that a remarkable hyperMaxwell-CS gravity theory without spin-4 gauge fields can be constructed, and whose underlying superalgebra results in a sub-superalgebra of one of the hyper-Maxwell algebras that include spin-4 generators, which transform in an spin-3 irreducible representation of the Lorentz group.
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