Asymptotically flat structure of hypergravity in three spacetime dimensions

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.

36 pages, no figures. Matches published version

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• The BMS/GCA correspondence
• Galilean Conformal Algebras and AdS/CFT
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• Generalized Black Holes in Three-dimensional Spacetime
• Asymptotic symmetries and dynamics of three-dimensional flat supergravity
• Three-dimensional supergravity reloaded
• Flat space (higher spin) gravity with chemical potentials
• Higher spin extension of cosmological spacetimes in 3D: asymptotically flat behaviour with chemical potentials and thermodynamics
• Extension of the Poincaré group with half-integer spin generators: hypergravity and beyond
• Quantization of conical spaces in 3D gravity
• Hypersymmetry bounds and three-dimensional higher-spin black holes
• Hypergravity in AdS_3

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