Extended anti-de Sitter Hypergravity in 2+1 Dimensions and Hypersymmetry Bounds

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In a recent paper (JHEP 1508 (2015) 021), we have investigated hypersymmetry bounds in the context of simple anti-de Sitter hypergravity in 2+1 dimensions. We showed that these bounds involved non linearly the spin-2 and spin-4 charges, and were saturated by a class of extremal black holes, which are 14-hypersymmetric. We continue the analysis here by considering (M,N)-extended anti-de Sitter hypergravity models, based on the superalgebra osp(M 4) ⊕ osp(N 4). The asymptotic symmetry superalgebra is then the direct sum of two-copies of a W-superalgebra that contains so(M) (or so(N)) Kac-Moody currents of conformal weight 1, fermionic generators of conformal weight 5/2 and bosonic generators of conformal weight 4 in addition to the Virasoro generators. The nonlinear hypersymmetry bounds on the conserved charges are derived and shown to be saturated by a class of extreme hypersymmetric black holes which we explicitly construct.