  We construct, to second order, the effective action of General Relativity for
small excitations generated by a vector field and use it to study conformal
symmetry in the boundary of AdS$_3$. By requiring finiteness of the boundary
effective action(s) for certain asymptotic transformations, we derive the
well-known Virasoro algebra and central charge associated with the boundary of
AdS$_3$. The bulk action for these transformations can be arbitrarily small.
