  We show that the recently proposed free boundary conditions for AdS$_3$ are
dual to two-dimensional quantum gravity in certain fixed gauges. In particular,
we note that an appropriate identification of the generator of Virasoro
transformations leads to a vanishing total central charge in agreement with the
theory at the boundary. We argue that this identification is necessary to match
the bulk and boundary generators of Virasoro transformations and for
consistency with the constraint equations.
