Asymptotically flat structure of hypergravity in three spacetime dimensions

TL;DR

The paper analyzes asymptotically flat three-dimensional hypergravity without a cosmological constant using a Chern–Simons formulation based on the hyper‑Poincaré algebra. It derives a nonlinear hypersymmetric extension of the $BMS_{3}$ algebra (hyper‑BMS$_{3}$) as the asymptotic symmetry and shows it arises from contraction of $W_{(2,4)}\oplus W_{(2,\frac{5}{2},4)}$, including central extensions from parity-odd terms. Hypersymmetry bounds are obtained from the fermionic anticommutator and saturate for spacetimes with unbroken hypersymmetries, identifying ground states such as the null orbifold or Minkowski depending on boundary conditions; the ground-state selection is tied to the sign of the bosonic charge $\mathcal{P}$. The framework is then extended to include parity-odd terms and to arbitrary half‑integer spins, with bounds given by polynomials of degree $s+\tfrac{1}{2}$ in the energy, providing a unified view of stability and symmetry in 3D hypergravity and a path toward higher-spin generalizations.

Abstract

The asymptotic structure of three-dimensional hypergravity without cosmological constant is analyzed. In the case of gravity minimally coupled to a spin-$5/2$ field, a consistent set of boundary conditions is proposed, being wide enough so as to accommodate a generic choice of chemical potentials associated to the global charges. The algebra of the canonical generators of the asymptotic symmetries is given by a hypersymmetric nonlinear extension of BMS$_{3}$. It is shown that the asymptotic symmetry algebra can be recovered from a subset of a suitable limit of the direct sum of the W$_{\left(2,4\right)}$ algebra with its hypersymmetric extension. The presence of hypersymmetry generators allows to construct bounds for the energy, which turn out to be nonlinear and saturate for spacetimes that admit globally-defined "Killing vector-spinors". The null orbifold or Minkowski spacetime can then be seen as the corresponding ground state in the case of fermions that fulfill periodic or anti-periodic boundary conditions, respectively. The hypergravity theory is also explicitly extended so as to admit parity-odd terms in the action. It is then shown that the asymptotic symmetry algebra includes an additional central charge, being proportional to the coupling of the Lorentz-Chern-Simons form. The generalization of these results in the case of gravity minimally coupled to arbitrary half-integer spin fields is also carried out. The hypersymmetry bounds are found to be given by a suitable polynomial of degree $s+\frac{1}{2}$ in the energy, where $s$ is the spin of the fermionic generators.