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.
Highlights
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
The causal structure of these black holes is difficult to define given that the spacetime geometry associated with the metric is not invariant under the gauge transformations of the higher spin gauge fields, one can study their thermodynamics by considering the Euclidean continuation of the theory
In this article we have shown that hypersymmetry implies interesting bounds on the solutions of three-dimensional AdS hypergravity
Summary
AdS hypergravity in three-dimensional spacetimes with the minimum amount of hypersymmetry in each sector can be described as an osp(1|4) ⊕ osp(1|4) Chern-Simons theory. Following the lines of [4, 5, 27, 38], the asymptotic behaviour of the dynamical fields at a fixed time slice t = t0, is assumed to be such that deviations with respect to the reference background go along the highest weight generators, i.e., a±φ. These fall-off conditions are maintained under a restricted set of gauge transformations, δa± = dΩ± + [a±, Ω±], where each of the Lie-algebra-valued parameters.
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