  We generalize the holographic correspondence between topological gravity
coupled to an abelian Chern-Simons theory in three dimensions and an ensemble
average of Narain's family of massless free bosons in two dimensions,
discovered by Afkhami-Jeddi et al. and by Maloney and Witten. We find that the
correspondence also works for toroidal orbifolds but not for K3 or Calabi-Yau
sigma-models and not always for the minimal models. We conjecture that the
correspondence requires that the central charge is equal to the critical
central charge defined by the asymptotic density of states of the chiral
algebra. For toroidal orbifolds, we extend the holographic correspondence to
correlation functions of twist operators by using topological properties of
rational tangles in the three-dimensional ball, which represent configurations
of vortices associated to a discrete gauge symmetry.
