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 (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.

On the supersymmetric extension of asymptotic symmetries in three spacetime dimensions

“…An S-expanded super-Virasoro algebra can be obtained by considering a semigroup S = {λ i } such that the new algebra is given by the direct product S × svir. The expanded generators are given in terms of the super-Virasoro ones as 11) and satisfy the (anti-)commutation relations…”

“…In the vanishing-cosmological constant case, the symmetry of asymptotically flat spacetimes at null infinity is described by the BM S 3 algebra [2][3][4] which is the three-dimensional version of the BM S algebra introduced more than a half century ago [5,6]. Extensions of the BM S 3 symmetry have been subsequently studied in [7][8][9][10][11][12][13][14][15][16].…”

Three-dimensional (higher-spin) gravities with extended Schrödinger and l-conformal Galilean symmetries

“…Curiously, this is exactly the condition on the structure constants in the odd sector of a hyper-Poincaré algebra [51], a higher-spin generalization of the conventional Poincaré supersymmetry algebra first introduced in [14]. This restriction implies that the structure constants should satisfy a recurrence relation…”

“…In [51] it was pointed out that the structure constants f (l) p,q can be expressed via homogeneous polynomials. In the same manner N p,q can also be presented as polynomials.…”

“…In the case of a generic half-integer l the number of the generators C i p are equal to the number of independent components of a symmetric gamma-traceless tensor Z a 1 ...ani α with n = l − 1 2 . Hence, by analogy with the hyper-Poincaré algebras [51], we can present the extended l-conformal Galilean algebra in the following form:…”