Boundary conditions for General Relativity on AdS$_{3}$ and the KdV hierarchy

Understand

It is shown that General Relativity with negative cosmological constant in three spacetime dimensions admits a new family of boundary conditions being labeled by a nonnegative integer $k$.

• Gravitational excitations are then described by "boundary gravitons" that fulfill the equations of the $k$-th element of the KdV hierarchy.
• In particular, $k=0$ corresponds to the Brown-Henneaux boundary conditions so that excitations are described by chiral movers.
• In the case of $k=1$, the boundary gravitons fulfill the KdV equation and the asymptotic symmetry algebra turns out to be infinite-dimensional, abelian and devoid of central extensions.