Hypersymmetry bounds and three-dimensional higher-spin black holes

TL;DR

This paper derives hypersymmetry bounds in three-dimensional higher-spin anti-de Sitter gravity, identifying extremal black hole solutions that saturate these bounds and possess partial hypersymmetry.

Contribution

It provides the first detailed analysis of hypersymmetry bounds in higher-spin AdS gravity, revealing the structure of extremal black holes with partial hypersymmetry.

Findings

Hypersymmetry bounds are nonlinear and derived from superalgebra anticommutators.

Extremal black holes saturate the bounds and have 1/4 hypersymmetry.

Extended analysis includes maximally symmetric solitonic solutions.

Abstract

We investigate the hypersymmetry bounds on the higher spin black hole parameters that follow from the asymptotic symmetry superalgebra in higher-spin anti-de Sitter gravity in three spacetime dimensions. We consider anti-de Sitter hypergravity for which the analysis is most transparent. This is a $osp(1\vert 4) \oplus osp(1\vert 4)$ Chern-Simons theory which contains, besides a spin-$2$ field, a spin-$4$ field and a spin-$5/2$ field. The asymptotic symmetry superalgebra is then the direct sum of two-copies of the hypersymmetric extension $W_{(2,\frac52,4)}$ of $W_{(2,4)}$, which contains fermionic generators of conformal weight $5/2$ and bosonic generators of conformal weight $4$ in addition to the Virasoro generators. Following standard methods, we derive bounds on the conserved charges from the anticommutator of the hypersymmetry generators. The hypersymmetry bounds are nonlinear and are saturated by the hypersymmetric black holes, which turn out to possess $1/4$-hypersymmetry and to be "extreme", where extremality can be defined in terms of the entropy: extreme black holes are those that fulfill the extremality bounds beyond which the entropy ceases to be a real function of the black hole parameters. We also extend the analysis to other $sp(4)$-solitonic solutions which are maximally (hyper)symmetric.