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

Understand

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.