# Asymptotic structure of $\mathcal{N}=2$ supergravity in 3D: extended super-BMS3 and nonlinear energy bounds

Journal of High Energy Physics, Sep 2017

The asymptotically flat structure of $\mathcal{N}=\left(2,0\right)$ 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 û(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 BMS3 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 the û(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-like û(1) charge, the energy becomes bounded from below by the energy of the ground state shifted by the square of the electric-like û(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 $\mathcal{N}=2$ super-Virasoro algebra. Indeed, our supersymmetric extension of BMS3 can be recovered from the Inönü-Wigner contraction of the superconformal algebra with $\mathcal{N}=\left(2,2\right)$, once the fermionic generators of the right copy are truncated.

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Oscar Fuentealba, Javier Matulich, Ricardo Troncoso. Asymptotic structure of $\mathcal{N}=2$ supergravity in 3D: extended super-BMS3 and nonlinear energy bounds, Journal of High Energy Physics, 2017, 30, DOI: 10.1007/JHEP09(2017)030