Extension of the Poincar\'e group with half-integer spin generators: hypergravity and beyond

TL;DR

This paper constructs an extension of the Poincaré group with half-integer spin generators, explores its application to hypergravity in three dimensions, and discusses possible higher-dimensional generalizations and infinite-dimensional extensions.

Contribution

It explicitly constructs a new algebra extending the Poincaré group with half-integer spins and demonstrates its application to hypergravity and potential higher-dimensional theories.

Findings

Hypergravity can incorporate the extended algebra as a local gauge symmetry.

The algebra admits a nontrivial Casimir operator allowing a Chern-Simons formulation.

An infinite-dimensional non-linear extension related to WB2 is identified.

Abstract

An extension of the Poincar\'e 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 Poincar\'e 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 Poincar\'e group can be extended with half-integer spin generators for $d\geq3$ dimensions.