Conical Defects, Black Holes and Higher Spin (Super-)Symmetry

Abstract

We study the (super-)symmetries of classical solutions in the higher spin (super-)gravity in AdS${}_3$. We show that the symmetries of the solutions are encoded in the holonomy around the spatial circle. When the spatial holonomies of the solutions are trivial, they preserve maximal symmetries of the theory, and are actually the smooth conical defects. We find all the smooth conical defects in the $sl(N),so(2N+1),sp(2N),so(2N),g_2$, as well as in $sl(N|N-1)$ and $osp(2N+1|2N)$ Chern-Simons gravity theories. In the bosonic higher spin cases, there are one-to-one correspondences between the smooth conical defects and the highest weight representations of Lie group. Furthermore we investigate the higher spin black holes in $osp(3|2)$ and $sl(3|2)$ higher spin (super-)gravity and find that they are only partially symmetric. In general, the black holes break all the supersymmetries, but in some cases they preserve part of the supersymmetries.

48 pages; more clarifications on conical defects in supersymmetric case

References in corpus (10)

• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• Thermodynamics of higher spin black holes in 3D
• The semiclassical limit of W_N CFTs and Vasiliev theory
• Even spin minimal model holography
• Conical defects and N=2 higher spin holography
• Phase Structure of Higher Spin Black Hole
• Dualities from higher-spin supergravity
• A semi-local holographic minimal model
• D2 Chern-Simons Gravity

Cited by in corpus (21)

• Asymptotic structure of $\mathcal{N}=2$ supergravity in 3D: extended super-BMS${}_3$ and nonlinear energy bounds
• Higher spin extension of cosmological spacetimes in 3D: asymptotically flat behaviour with chemical potentials and thermodynamics
• Probing higher spin black holes from CFT
• Extension of the Poincaré group with half-integer spin generators: hypergravity and beyond
• Asymptotically flat structure of hypergravity in three spacetime dimensions
• Conformal blocks from Wilson lines with loop corrections
• Hypersymmetry bounds and three-dimensional higher-spin black holes
• Correlators in higher spin AdS_3 holography from Wilson lines with loop corrections
• The $\mathcal{N}=1$ algebra ${\mathcal{W}}_{\infty }[\mu ]$ and its truncations
• Superconformal blocks from Wilson lines with loop corrections
• Modular Properties of 3D Higher Spin Theory
• On the partition functions of higher spin black holes
• Black holes in higher spin supergravity
• Hypersymmetric extensions of Maxwell Chern-Simons gravity in (2+1) dimensions
• Extremal Higher Spin Black Holes
• Exploring new Boundary Conditions for $\mathcal{N}=(1,1)$ Extended Higher Spin $Ad{S}_3$ Supergravity
• $\mathcal{N}=(2,2)$ extended $\mathfrak{sl}(3|2)$ Chern-Simons $Ad{S}_3$ supergravity with new boundaries
• Hypergravity in five dimensions
• A note on the $\mathcal{N}=2$ super-${\mathcal{W}}_3$ holographic dictionary
• Four dimensional topological supergravities from transgression field theory
• Higher Spin Chern-Simons Theory and the Super Boussinesq hierarchy