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

TL;DR

This paper explores the boundary dynamics of Einstein gravity on AdS3 with KdV-type boundary conditions, revealing an integrable, non-relativistic dual field theory governed by potential modified KdV equations and Lifshitz scaling.

Contribution

It introduces a novel boundary action principle for AdS3 gravity with KdV boundary conditions, establishing its integrability and non-relativistic Lifshitz-like features.

Findings

Boundary dual is a 2D integrable field theory

Infinite conserved charges from asymptotic symmetries

Boundary theory exhibits Lifshitz scaling

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.