Abstract:  It is shown that General Relativity with negative cosmological constant in 3D 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 kth element of the KdV hierarchy. In particular, k = 0 corresponds to the BrownHenneaux 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 infinitedimensional, abelian and devoid of central extensions. The latter feature also holds for the remaining cases that describe the hierarchy (k > 1). Our boundary conditions then provide a gravitational dual of two noninteracting left and right KdV movers, and hence, boundary gravitons possess anisotropic Lifshitz scaling with dynamical exponent z = 2k + 1. Remarkably, despite spacetimes solving the field equations are locally AdS, they possess anisotropic scaling being induced by the choice of boundary conditions. As an application, the entropy of a rotating BTZ black hole is precisely recovered from a suitable generalization of the Cardy formula that is compatible with the anisotropic scaling of the chiral KdV movers at the boundary. The relation between this new set of boundary conditions for threedimensional gravity on AdS_3 and the generalized Gibbs ensemble of twodimensional CFTs will be also discussed.
