Abstract:The asymptotically flat structure of N = (2, 0) supergravity in three spacetime dimensions is explored. The asymptotic symmetries are found to be spanned by an extension of the super-BMS 3 algebra, endowed with two independent affineû(1) currents of electric and magnetic type. These currents are associated to U(1) fields being even and odd under parity, respectively. Remarkably, although the U(1) fields do not generate a backreaction on the metric, they provide nontrivial Sugawara-like contributions to the BMS 3 generators, and hence to the energy and the angular momentum. Consequently, the entropy of flat cosmological spacetimes endowed with U(1) fields acquires a nontrivial dependence on the zero modes of theû(1) charges. If the spin structure is odd, the ground state corresponds to Minkowski spacetime, and although the anticommutator of the canonical supercharges is linear in the energy and in the electric-likeû(1) charge, the energy becomes bounded from below by the energy of the ground state shifted by the square of the electric-likeû(1) charge. If the spin structure is even, the same bound for the energy generically holds, unless the absolute value of the electric-like charge is less than minus the mass of Minkowski spacetime in vacuum, so that the energy has to be nonnegative. The explicit form of the global and asymptotic Killing spinors is found for a wide class of configurations that fulfills our boundary conditions, and they exist precisely when the corresponding bounds are saturated. It is also shown that the spectra with periodic or antiperiodic boundary conditions for the fermionic fields are related by spectral flow, in a similar way as it occurs for the N = 2 super-Virasoro algebra. Indeed, our supersymmetric extension of BMS 3 can be recovered from the Inönü-Wigner contraction of the superconformal algebra with N = (2, 2), once the fermionic generators of the right copy are truncated.

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 ≥ 3 dimensions.

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 (2,4) 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 antiperiodic 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 + 1 2 in the energy, where s is the spin of the fermionic generators.