Revisiting the asymptotic dynamics of General Relativity on AdS${}_3$

Abstract

The dual dynamics of Einstein gravity on AdS${}_3$ supplemented with boundary conditions of KdV-type is identified. It corresponds to a two-dimensional field theory at the boundary, described by a novel action principle whose field equations are given by two copies of the "potential modified KdV equation". The asymptotic symmetries then transmute into the global Noether symmetries of the dual action, giving rise to an infinite set of commuting conserved charges, implying the integrability of the system. Noteworthy, the theory at the boundary is non-relativistic and possesses anisotropic scaling of Lifshitz type.

arXiv comment18 pages

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Cited by in corpus (15)

• Geometric actions and flat space holography
• Near horizon dynamics of three dimensional black holes
• Boundary conditions for General Relativity in three-dimensional spacetimes, integrable systems and the KdV/mKdV hierarchies
• Asymptotic dynamics of AdS${}_3$ gravity with two asymptotic regions
• New boundary conditions for (extended) ${\mathrm{AdS}}_3$ supergravity
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• Gravity coupled to a scalar field from a Chern-Simons action: describing rotating hairy black holes and solitons with gauge fields
• BTZ black hole with KdV-type boundary conditions: Thermodynamics revisited
• The anisotropic chiral boson
• Higher Spin Gravity in $Ad{S}_3$ and Folds on Fermi Surface
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