Ensemble averaging torus orbifolds

 We generalize the recent holographic correspondence between an ensemble average of free bosons in two dimensions, and a Chern-Simons-like theory of gravity in three dimensions, by Afkhami-Jeddi et al and Maloney and Witten. We find that the correspondence also works for toroidal orbifolds, but we run into difficulties generalizing to K3 and Calabi-Yau sigma models. For the case of toroidal orbifolds, we extend the holographic correspondence to averages of correlation functions of twist operators by using properties of rational tangles in three-dimensional balls and their covering spaces. Based on work to appear with C. Keller, H. Ooguri, and I. Zadeh.