New Boundary Conditions for \(AdS_3\)

Abstract

New chiral boundary conditions are found for quantum gravity with matter on \(AdS_3\). The associated asymptotic symmetry group is generated by a single right-moving U(1) Kac-Moody-Virasoro algebra with \(c_R=\frac{3ℓ}{2G}\). The Kac-Moody zero mode generates global left-moving translations and equals, for a BTZ black hole, the sum of the total mass and spin. The level is positive about the global vacuum and negative in the black hole sector, corresponding to ergosphere formation. Realizations arising in Chern-Simons gravity and string theory are analyzed. The new boundary conditions are shown to naturally arise for warped \(AdS_3\) in the limit that the warp parameter is taken to zero.