Extension of the Poincaré group with half-integer spin generators: hypergravity and beyond

TL;DR

The paper constructs a hyper-Poincaré extension of the Poincaré group by half-integer spin generators in three dimensions and develops a Chern-Simons gauge formulation to describe hypergravity. It generalizes to fermionic generators of spin s = n + 1/2 using a Maurer-Cartan framework and identifies a nontrivial Casimir along with an invariant bilinear form, enabling off-shell gauge closure. A nonlinear extension of the asymptotic symmetry algebra that encompasses BMS3 is found, and the construction is extended to higher spacetime dimensions without enlarging the Lorentz group. The work provides a robust CS-based framework for coupling gravity to higher half-integer spin fields and points to broader implications for nonlinear realizations and holographic contexts.

Abstract

An extension of the Poincaré group with half-integer spin generators is explicitly constructed. We start discussing the case of three spacetime dimensions, and as an application, it is shown that hypergravity can be formulated so as to incorporate this structure as its local gauge symmetry. Since the algebra admits a nontrivial Casimir operator, the theory can be described in terms of gauge fields associated to the extension of the Poincaré group with a Chern-Simons action. The algebra is also shown to admit an infinite-dimensional non-linear extension, that in the case of fermionic spin-$3/2$ generators, corresponds to a subset of a contraction of two copies of WB$_2$. Finally, we show how the Poincaré group can be extended with half-integer spin generators for $d\geq3$ dimensions.