W Symmetry and Integrability of Higher spin black holes

Abstract

We obtain the asymptotic symmetry algebra of sl(3,R) x sl(3,R) Chern-Simons theory with Dirichlet boundary conditions for fixed chemical potential. These boundary conditions are obeyed by higher spin black holes. For each embedding of sl(2,R) into sl(3,R), we show that the asymptotic symmetry group is independent of the chemical potential. On the one hand, starting from AdS3 in the principal embedding, we show that the W3 x W3 symmetry is preserved upon turning on perturbatively spin 3 chemical potentials. On the other hand, starting from AdS3 in the diagonal embedding, we show that the W3^(2) x W3^(2) symmetry is preserved upon turning on finite spin 3/2 chemical potentials. We also make connections between the canonical Lagrangian formalism and integrability methods based on the third KdV (Boussinesq) hierarchy.

40 pages, typos corrected, refs added, published version

References in corpus (9)

• 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
• Surface charge algebra in gauge theories and thermodynamic integrability
• Symmetries of Holographic Minimal Models
• Large N=4 Holography
• Central Charge for AdS_2 Quantum Gravity
• Even spin minimal model holography
• N=1 extension of minimal model holography
• Asymptotic symmetries and thermodynamics of higher spin black holes in AdS3

Cited by in corpus (37)

• Wilson Lines and Entanglement Entropy in Higher Spin Gravity
• Generalized Black Holes in Three-dimensional Spacetime
• Symplectic and Killing Symmetries of AdS${}_3$ Gravity: Holographic vs Boundary Gravitons
• Boundary conditions for General Relativity on AdS${}_3$ and the KdV hierarchy
• Entanglement Entropy and Higher Spin Holography in AdS${}_3$
• Chemical potentials in three-dimensional higher spin anti-de Sitter gravity
• Higher Spin Black Holes with Soft Hair
• Higher spin entanglement entropy from CFT
• Observables and Microscopic Entropy of Higher Spin Black Holes
• Flat space (higher spin) gravity with chemical potentials
• Higher spin extension of cosmological spacetimes in 3D: asymptotically flat behaviour with chemical potentials and thermodynamics
• Probing higher spin black holes from CFT
• Generalized Chern-Simons higher-spin gravity theories in three dimensions
• Lifshitz black holes in higher spin gravity
• Boundary Conditions and Partition Functions in Higher Spin AdS${}_3$/CFT${}_2$
• Conformal perturbation theory and higher spin entanglement entropy on the torus
• Integrable systems with BMS${}_3$ Poisson structure and the dynamics of locally flat spacetimes
• Revisiting the asymptotic dynamics of General Relativity on AdS${}_3$
• Brief review on higher spin black holes
• Non-relativistic and Ultra-relativistic Expansions of Three-dimensional Spin-3 Gravity Theories
• Modular Properties of 3D Higher Spin Theory
• How General Is Holography?
• A new spin on entanglement entropy
• On the partition functions of higher spin black holes
• Higher spin entanglement entropy at finite temperature with chemical potential
• Higher Spin Lifshitz Theories and the KdV-Hierarchy
• Higher Spin Lifshitz Theory and Integrable Systems
• Black Holes in the 3D Higher Spin Theory and Their Quasi Normal Modes
• Analysis of higher spin black holes with spin-4 chemical potential
• Relative entropy in higher spin holography
• The covariant action of higher spin black holes in three dimensions
• Higher Spin Gravity in $Ad{S}_3$ and Folds on Fermi Surface
• Phase space holography with no strings attached
• Holographic chiral induced W-gravities
• Null warped AdS in higher spin gravity
• Asymptotic structure of three-dimensional Maxwell Chern-Simons gravity coupled to spin-3 fields
• About the phase space of SL(3) Black Holes