Asymptotic structure of N=2 supergravity in 3D: extended super-BMS3 and nonlinear energy bounds
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-BMS3 algebra, endowed with two independent affine u(1) currents of electric and magnetic type. These currents are associated to U(1) fields that are even and odd under parity, respectively. Remarkably, although the U(1) fields do not generate a backreaction on the metric, they give nontrivial Sugawara-like contributions to the BMS3 generators, and hence to the energy and the angular momentum. Consequently, it can be seen that the entropy of flat cosmological spacetimes endowed with U(1) fields not only depends on the mass and the angular momentum but also on the zero modes of the u(1) charges. We also show that in the case where the spin structure is chosen to be even, the energy is shown to be nonnegative, while if the spin structure is odd, the ground state corresponds to Minkowski spacetime. Additionally, although the anticommutator of the canonical supercharges is linear in the energy and in the electric-like u(1) charge, the energy becomes bounded from below by the ground state energy shifted by a quadratic function of the electric-like u(1) charge. The explicit form of the (asymptotic) Killing spinors is also found for a wide class of configurations that fulfills our boundary conditions, and they are shown to exist precisely when the bounds are saturated. It is also shown that the spectra with periodic or antiperiodic boundary conditions for the fermions are related by spectral flow, in a similar way as it occurs for the N=2 super-Virasoro algebra. Indeed, our supersymmetric extension of BMS3 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.