A consistent set of asymptotic conditions for higher spin gravity in three dimensions is proposed in the case of vanishing cosmological constant. The asymptotic symmetries are found to be spanned by a higher spin extension of the BMS3 algebra with an appropriate central extension. It is also shown that our results can be recovered from the ones recently found for asymptotically AdS3 spacetimes by virtue of a suitable gauge choice that allows to perform the vanishing cosmological constant limit.
A consistent set of asymptotic conditions for the simplest supergravity theory without cosmological constant in three dimensions is proposed. The canonical generators associated to the asymptotic symmetries are shown to span a supersymmetric extension of the BMS3 algebra with an appropriate central charge. The energy is manifestly bounded from below with the ground state given by the null orbifold or Minkowski spacetime for periodic, respectively antiperiodic boundary conditions on the gravitino. These results are related to the corresponding ones in AdS3 supergravity by a suitable flat limit. The analysis is generalized to the case of minimal flat supergravity with additional parity odd terms for which the Poisson algebra of canonical generators form a representation of the super-BMS3 algebra with an additional central charge.
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.
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