Integrable systems and the boundary dynamics of higher spin gravity on AdS${}_3$

Abstract

We introduce a new set of boundary conditions for three-dimensional higher spin gravity with gauge group $SL(3,\mathbb{R})\times SL(3,\mathbb{R})$, where its dynamics at the boundary is described by the members of the modified Boussinesq integrable hierarchy. In the asymptotic region the gauge fields are written in the diagonal gauge, where the excitations go along the generators of the Cartan subalgebra of $sl(3,\mathbb{R})\oplus sl(3,\mathbb{R})$. We show that the entire integrable structure of the modified Boussinesq hierarchy, i.e., the phase space, the Poisson brackets and the infinite number of commuting conserved charges, are obtained from the asymptotic structure of the higher spin theory. Furthermore, its known relation with the Boussinesq hierarchy is inherited from our analysis once the asymptotic conditions are re-expressed in the highest weight gauge. Hence, the Miura map is recovered from a purely geometric construction in the bulk. Black holes that fit within our boundary conditions, the Hamiltonian reduction at the boundary, and the generalization to higher spin gravity with gauge group $SL(N,\mathbb{R})\times SL(N,\mathbb{R})$ are also discussed.

arXiv comment28 pages, no figures. Minor corrections and references added. Matches published version

References in corpus (44)

• Nonlinear Fluid Dynamics from Gravity
• Quantum Quench in the Transverse Field Ising Chain
• Nonlinear Equations for Symmetric Massless Higher Spin Fields in $(A)d{S}_d$
• Complete Generalized Gibbs Ensemble in an interacting Theory
• 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
• Integrable Structure of Conformal Field Theory, Quantum KdV Theory and Thermodynamic Bethe Ansatz
• Higher-Spin Gauge Theories in Four, Three and Two Dimensions
• Higher Spin Black Holes
• Spacetime Geometry in Higher Spin Gravity
• Validity of the GGE for quantum quenches from interacting to noninteracting models
• New Boundary Conditions for AdS3
• Asymptotic Dynamics and Asymptotic Symmetries of Three-Dimensional Extended AdS Supergravity
• Soft Heisenberg hair on black holes in three dimensions
• Conformal Nonlinear Fluid Dynamics from Gravity in Arbitrary Dimensions
• Averaging Over Narain Moduli Space
• Higher spin theory in 3-dimensional flat space
• Asymptotically flat spacetimes in three-dimensional higher spin gravity
• Generalized Black Holes in Three-dimensional Spacetime
• Most general AdS_3 boundary conditions
• Nonlinear viscous hydrodynamics in various dimensions using AdS/CFT
• Enhanced asymptotic symmetry algebra of AdS3
• Boundary conditions for General Relativity on AdS${}_3$ and the KdV hierarchy
• Chemical potentials in three-dimensional higher spin anti-de Sitter gravity
• Two-dimensional fluids and their holographic duals
• Higher Spin Black Holes with Soft Hair
• An sl(2, R) current algebra from AdS_3 gravity
• Generalized Eigenstate Thermalization in 2d CFTs
• Flat space (higher spin) gravity with chemical potentials
• Higher spin extension of cosmological spacetimes in 3D: asymptotically flat behaviour with chemical potentials and thermodynamics
• Comments on Thermalization in 2D CFT
• Higher-Spin Flat Space Cosmologies with Soft Hair
• Extension of the Poincaré group with half-integer spin generators: hypergravity and beyond
• Asymptotically flat structure of hypergravity in three spacetime dimensions
• Near horizon dynamics of three dimensional black holes
• Thermal Correlation Functions of KdV Charges in 2D CFT
• Boundary conditions for General Relativity in three-dimensional spacetimes, integrable systems and the KdV/mKdV hierarchies
• Gravitational dual of averaged free CFT's over the Narain lattice
• Hypersymmetry bounds and three-dimensional higher-spin black holes
• Integrable systems with BMS${}_3$ Poisson structure and the dynamics of locally flat spacetimes
• Asymptotic dynamics of AdS${}_3$ gravity with two asymptotic regions
• Revisiting the asymptotic dynamics of General Relativity on AdS${}_3$
• KdV-charged black holes
• Lifshitz Scaling, Microstate Counting from Number Theory and Black Hole Entropy

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