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

TL;DR

This paper extends the study of hypersymmetry bounds in 2+1 dimensional anti-de Sitter hypergravity to include $(M,N)$-extended models, deriving bounds saturated by extremal hypersymmetric black holes with a detailed algebraic structure.

Contribution

It introduces $(M,N)$-extended anti-de Sitter hypergravity models based on $osp(M|4) imes osp(N|4)$ and derives nonlinear hypersymmetry bounds saturated by explicit extremal black hole solutions.

Findings

Derived nonlinear hypersymmetry bounds for extended models.

Constructed explicit extremal hypersymmetric black hole solutions.

Analyzed the asymptotic symmetry superalgebra structure.

Abstract

In a recent paper (JHEP {\bf 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 $\frac14$-hypersymmetric. We continue the analysis here by considering $(M,N)$-extended anti-de Sitter hypergravity models, based on the superalgebra $osp(M \vert 4) \oplus osp(N \vert 4)$. 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.